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Exceptional points (EPs)—singularities in the parameter space of non-Hermitian systems where two nearby eigenmodes coalesce—feature unique properties with applications such as sensitivity enhancement and chiral emission. Existing realizations of EP lasers operate with static populations in the gain medium. By analyzing the full-wave Maxwell–Bloch equations, here we show that in a laser operating sufficiently close to an EP, the nonlinear gain will spontaneously induce a multi-spectral multi-modal instability above a pump threshold, which initiates an oscillating population inversion and generates a frequency comb. The efficiency of comb generation is enhanced by both the spectral degeneracy and the spatial coalescence of modes near an EP. Such an "EP comb" has a widely tunable repetition rate, self-starts without external modulators or a continuous-wave pump, and can be realized with an ultra-compact footprint. We develop an exact solution of the Maxwell–Bloch equations with an oscillating inversion, describing all spatiotemporal properties of the EP comb as a limit cycle. We numerically illustrate this phenomenon in a 5-μm-long gain-loss coupled AlGaAs cavity and adjust the EP comb repetition rate from 20 to 27 GHz. This work provides a rigorous spatiotemporal description of the rich laser behaviors that arise from the interplay between the non-Hermiticity, nonlinearity, and dynamics of a gain medium. An ab initio laser theory is developed to show that exceptional-point lasers can self-generate frequency combs through dynamic population inversion. Notably, the repetition rate of these EP combs is independent of the cavity's free spectral range. [ABSTRACT FROM AUTHOR]

This research work focusses on examining the attributes of ion-acoustic waves (IA waves) in a plasma environment embodying superthermal-trapped electron distributions, characterised by the parameters κ and β representing superthermality and trapping respectively. The study utilises a modified nonlinear Schrödinger equation (m-NLSE) derived using the reductive perturbation method (RPM) to model the dynamics of modulated wave packets in this plasma framework. The study investigates the impact of superthermality (κ ) and trapping (β ) parameters on the envelopes of IA waves. The research explores the conditions for modulational instability (MI) of IA waves, characterised by the dispersion-nonlinearity product PQ in the m-NLSE. Bright and dark solitons are observed corresponding to different signs of PQ, i.e., P Q < 0 and P Q > 0 indicating the presence of modulationally unstable and stable regimes, respectively. The cutoff wavenumber k c at which MI enters increases with decreasing superthermality (increasing κ ). Interestingly, k c is observed to be independent of the trapping parameter (β ), suggesting that electron trapping does not significantly influence the onset of MI. Further, the effects of κ and β on the maximum growth rate ( Γ max ) and the modulational wavenumber ( K max ) associated with MI are also investigated. [ABSTRACT FROM AUTHOR]

The hydrodynamic stability behavior of a two-layer falling film is explored with a floating flexible plate on the top layer surface. The stress balance at the surface is modeled using a modified membrane equation. There is an insoluble surfactant at the liquid-liquid interface of the flow system. The linear instability of perturbation waves is captured by numerically solving the generalized Orr-Sommerfeld eigenvalue problem using the Chebyshev spectral collocation technique. Four different types of linear stability modes are identified: surface mode (SM), interface mode (IM), interface surfactant mode (ISM), and shear mode (SHM). The floating flexible plate has an inferior impact on all the existing modes in the longwave zone. However, a significant influence is noticed for the finite wave numbers. The surface and interface wave instabilities can be suppressed in the smaller wavenumber zone by imposing higher structural rigidity and uniform thickness of the flexible plate. The stabilizing nature of the surface mode becomes more powerful when the top layer viscosity is dominant. A new interfacial instability emerges when the top layer is less viscous than the lower one. At moderate Reynolds numbers, the behavior of interface mode is different in two different zones m r < 1 and m r > 1 , where m and r denote the viscosity and density ratio, respectively. Further, the unstable shear modes induced by the top and bottom layers are detected under the low inclination angles with a strong inertia force. The occurrence of the shear modes requires the viscosity and density of the lower layer to be much higher than those of the upper layer. The influence of characteristic parameters of the flexible plate on the lower layer shear mode is not very sensitive. Finally, the competition between the different modes for dominance of stability boundaries is also discussed. • The hydrodynamic stability of a two-layer falling film is explored with a floating flexible plate on the top surface. • The generalized Orr-Sommerfeld eigenvalue problem is solved using Chebyshev spectral collocation technique. • Four modes, known as surface, interface, interface surfactant, and shear modes are detected. • The flexible plate has an inferior impact in the longwave zone, but significant effect in the finite wave number zone. • The plate's rigidity and thickness suppress the surface and interface wave instability in the smaller wavenumber zone. [ABSTRACT FROM AUTHOR]

The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the field of nonlinear dispersive equations. In this work, we investigate this topic in the context of focusing nonlinear Schrödinger (NLS) equations. In particular, we consider non-integrable counterparts of the (integrable) focusing cubic NLS equation, which are distinct generalizations of cubic NLS and involve a broad class of nonlinearities, with the cases of power and saturable nonlinearities serving as illustrative examples. This is a notably different direction from the one explored in other works, where the non-integrable models considered are only small perturbations of the integrable one. We study the Cauchy problem on the real line for both vanishing and non-vanishing boundary conditions at infinity and quantify the proximity of solutions between the integrable and non-integrable models via estimates in appropriate metrics as well as pointwise. These results establish that the distance of solutions grows at most linearly with respect to time, while the growth rate of each solution is chiefly controlled by the size of the initial data and the nonlinearity parameters. A major implication of these closeness estimates is that integrable dynamics emerging from small initial conditions may persist in the non-integrable setting for significantly long times. In the case of zero boundary conditions at infinity, this persistence includes soliton and soliton collision dynamics, while in the case of nonzero boundary conditions at infinity, it establishes the nonlinear behavior of the non-integrable models at the early stages of the ubiquitous phenomenon of modulational instability. For this latter and more challenging type of boundary conditions, the closeness estimates are proved with the aid of new results concerning the local existence of solutions to the non-integrable models. In addition to the infinite line, we also consider the cubic NLS equation and its non-integrable generalizations in the context of initial-boundary value problems on a finite interval. Apart from their own independent interest and features such as global existence of solutions (which does not occur in the infinite domain setting), such problems are naturally used to numerically simulate the Cauchy problem on the real line, thereby justifying the excellent agreement between the numerical findings and the theoretical results of this work. [ABSTRACT FROM AUTHOR]

Optical rogue waves are a nonlinear phenomenon that offers a unique opportunity to gain fundamental insights into wave interaction and behavior, and the evolution of complex systems. Optical systems serve as a suitable testbed for the well-controlled investigation of this natural phenomenon, which cannot be easily studied in an ocean environment. Additionally, such systems offer practical applications in telecommunications and optical signal processing, making this topic a vital area of research. Fiber lasers are considered the best candidates for demonstrating and investigating the emergence of optical rogue waves. In particular, they offer significant advantages in nonlinear dynamics due to faster field evolution and a higher number of events that can be recorded within a relatively short time. In this paper, we present the development mechanisms of optical rogue wave events. It was found that multimode vector instability, pulse–pulse interaction, and soliton rain are the main nonlinear dynamics leading to the formation of optical rogue wave events. [ABSTRACT FROM AUTHOR]

Numerical simulations have been an increasingly important tool in space physics. Here, we introduce an open-source three-dimensional compressible Hall-Magnetohydrodynamic (MHD) simulation code LAPS (UCLA-Pseudo-Spectral, https://github.com/chenshihelio/LAPS). The code adopts a pseudo-spectral method based on Fourier Transform to evaluate spatial derivatives, and third-order explicit Runge-Kutta method for time advancement. It is parallelized using Message-Passing-Interface (MPI) with a "pencil" parallelization strategy and has very high scalability. The Expanding-Box-Model is implemented to incorporate spherical expansion effects of the solar wind. We carry out test simulations based on four classic (Hall)-MHD processes, namely, 1) incompressible Hall-MHD waves, 2) incompressible tearing mode instability, 3) Orszag-Tang vortex, and 4) parametric decay instability. The test results agree perfectly with theory predictions and results of previous studies. Given all its features, LAPS is a powerful tool for large-scale simulations of solar wind turbulence as well as other MHD and Hall-MHD processes happening in space. [ABSTRACT FROM AUTHOR]

Feature detection and matching is the key technique for remote sensing image processing and related applications. In this paper, a PDE-constrained optimization model is proposed to determine the scale levels advantageous for feature detection. A variance estimation technique is introduced to treat the observation optical images polluted by additive zero-mean Gaussian noise and determine the parameter of a nonlinear scale space governed by the partial differential equation. Additive Operator Splitting is applied to efficiently solve the PDE constraint, and an iterative algorithm is proposed to approximate the optimal subset of the original scale level set. The selected levels are distributed more uniformly in the total variation sense and helpful for generating more accurate and robust feature points. The experimental results show that the proposed method can achieve about a 30% improvement in the number of correct matches with only a small increase in time cost. [ABSTRACT FROM AUTHOR]

The time-fractional coupled Drinfel'd–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, which works with one variable, and the Ω ′ Ω ,   1 Ω method which utilizes two variables. These approaches supply significant improvements in efficiency, accuracy, and the ability to explore a broader spectrum of soliton solutions compared to traditional computational methods. By using these techniques, we construct a wide range of wave structures, including rational, trigonometric, and hyperbolic functions. Rigorous validation with Mathematica software 13.1 ensures precision, while dynamic visual representations illustrate soliton solutions with diverse patterns such as dark solitons, multiple dark solitons, singular solitons, multiple singular solitons, kink solitons, bright solitons, and bell-shaped patterns. These findings highlight the effectiveness of these methods in discovering new soliton solutions and supplying deeper insights into the DSW model's behavior. The novel soliton solutions obtained in this study significantly enhance our understanding of the DSW equation's underlying dynamics and offer potential applications across various scientific fields. [ABSTRACT FROM AUTHOR]

An essential mathematical structure that demonstrates the nonlinear short-wave movement across the ferromagnetic materials having zero conductivity in an exterior region is known as the fractional stochastic Kraenkel–Manna–Merle system. In this article, we extract abundant wave structure closed-form soliton solutions to the fractional stochastic Kraenkel–Manna–Merle system with some important analyses, such as bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability. This fractional system renders a substantial impact on signal transmission, information systems, control theory, condensed matter physics, dynamics of chemical reactions, optical fiber communication, electromagnetism, image analysis, species coexistence, speech recognition, financial market behavior, etc. The Sardar sub-equation approach was implemented to generate several genuine innovative closed-form soliton solutions. Additionally, phase portraiture of bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability were employed to monitor the qualitative characteristics of the dynamical system. A certain number of the accumulated outcomes were graphed, including singular shape, kink-shaped, soliton-shaped, and dark kink-shaped soliton in terms of 3D and contour plots to better understand the physical mechanisms of fractional system. The results show that the proposed methodology with analysis in comparison with the other methods is very structured, simple, and extremely successful in analyzing the behavior of nonlinear evolution equations in the field of fractional PDEs. Assessments from this study can be utilized to provide theoretical advice for improving the fidelity and efficiency of soliton dissemination. [ABSTRACT FROM AUTHOR]

Traditional visual detection methods that employ image data are often unstable due to environmental influences like lighting conditions. However, microfiber spectrometers are capable of capturing the specific wavelength characteristics of tail coal suspensions, effectively circumventing the instability caused by lighting variations. Utilizing spectral analysis techniques for detecting ash content in tail coal appears promising as a more stable method of indirect ash detection. In this context, this paper proposes a rapid detection method for the coal ash content in tailings suspensions based on absorption spectra and deep feature extraction. Initially, a preprocessing method, the inverse time weight function (ITWF), is presented, focusing on the intrinsic connection between the sedimentation phenomena of samples. This enables the model to learn and retain spectral time memory features, thereby enhancing its analytical capabilities. To better capture the spectral characteristics of tail coal suspensions, we designed the DSFN (DeepSpectraFusionNet) model. This model has an MSCR (multi-scale convolutional residual) module, addressing the conventional models' oversight of the strong correlation between adjacent wavelengths in the spectrum. This facilitates the extraction of relative positional information. Additionally, to uncover potential temporal relationships in sedimentation, we propose a CLSM-CS (convolutional long-short memory with candidate states) module, designed to strengthen the capturing of local information and sequential memory. Ultimately, the method employs a fused convolutional deep classifier to integrate and reconstruct both temporal memory and positional features. This results in a model that effectively correlates the ash content of suspensions with their absorption spectral characteristics. Experimental results confirmed that the proposed model achieved an accuracy of 80.65%, an F1-score of 80.45%, a precision of 83.43%, and a recall of 80.65%. These results outperformed recent coal recognition models and classical temporal models, meeting the high standards required for industrial on-site ash detection tasks. [ABSTRACT FROM AUTHOR]

Self-generated magnetic field and electron jet are observed when ultra-intense lasers (> 1 × 10 18 W / c m 2 ) interact with plasma. It is found that the self-generated magnetic field plays a significant role in the generation of electron jets. The generation mechanism of electron jets under the influence of a self-generated circular magnetic field is examined. It is revealed that magnetic modulation of self-generated magnetic fields can result in the collapse of these fields, consequently leading to the production of electron jets. Furthermore, it has been discovered that the velocity of the electron jets is associated with the maximum growth rate of the modulational instability. As the maximum growth rate of the modulational instability decreases, the velocity of the electron jets is reduced. The present work aids in getting a deeper understanding of the generation of electron jets in relativistic laser plasmas. [ABSTRACT FROM AUTHOR]

Transverse Mode Instability (TMI) that results from dynamic nonlinear thermo-optical scattering is the primary limitation to power scaling in high-power fiber lasers and amplifiers. It has been proposed that TMI can be suppressed by exciting multiple modes in a highly multimode fiber. We derive a semi-analytic frequency-domain theory of the threshold for the onset of TMI in narrowband fiber amplifiers under arbitrary multimode input excitation for general fiber geometries. Our detailed model includes the effect of gain saturation, pump depletion, and mode-dependent gain. We show that TMI results from the exponential growth of noise in all the modes at downshifted frequencies due to the thermo-optical coupling. The noise growth rate in each mode is given by the sum of signal powers in various modes weighted by pairwise thermo-optical coupling coefficients. We calculate thermo-optical coupling coefficients for all ∼ 1 0 4 pairs of modes in a standard circular multimode fiber and show that modes with large transverse spatial frequency mismatch are weakly coupled, resulting in a banded coupling matrix. This short-range behavior is due to the diffusive nature of the heat propagation, which mediates the coupling and leads to a lower noise growth rate upon multimode excitation compared to a single mode, resulting in significant TMI suppression. We find that the TMI threshold scales linearly with the number of modes that are excited asymptotically, leading to roughly an order of magnitude increase in the TMI threshold in an 82-mode fiber amplifier. [ABSTRACT FROM AUTHOR]

Pattern-illuminated Fourier ptychography (piFP) is an elegant combination of structured illumination imaging and a Fourier ptychographic algorithm with the ability to image beyond the diffraction limit of the employed optics. Artifact-free piFP super-resolution reconstruction requires a high level of stability in the illumination pattern. However, unpredictable pattern variation occurs in the presence of environment perturbation, intensity fluctuation, and pointing instability at the source, leading to declines in image reconstruction quality. To address this issue, we present an efficient and robust piFP algorithm based on low-rank approximation (LRA-piFP), which relaxes the requirement for the stability of illumination patterns. This LRA-piFP method can model frame-wise pattern variation during a full scan, thus improve the reconstruction quality significantly. We take numerical simulations and proof-of-principle experiments with both long-range imaging and microscopy for demonstrations. Results show that the LRA-piFP method can handle different kinds of pattern variation and outperforms other state-of-the-art techniques in terms of reconstruction quality and resolution improvement. Our method provides effective experimental robustness to piFP with a natural algorithmic extension, paving the way for its application in both macroscopic and microscopic imaging. [ABSTRACT FROM AUTHOR]

Segmentation methods based on convolutional neural networks (CNN) have achieved remarkable results in the field of medical image segmentation due to their powerful representation capabilities. However, for brain-tumor segmentation, owing to the significant variations in shape, texture, and location, traditional convolutional neural networks (CNNs) with limited convolutional kernel-receptive fields struggle to model explicit long-range (global) dependencies, thereby restricting segmentation accuracy and making it difficult to accurately identify tumor boundaries in medical imaging. As a result, researchers have introduced the Swin Transformer, which has the capability to model long-distance dependencies, into the field of brain-tumor segmentation, offering unique advantages in the global modeling and semantic interaction of remote information. However, due to the high computational complexity of the Swin Transformer and its reliance on large-scale pretraining, it faces constraints when processing large-scale medical images. Therefore, this study addresses this issue by proposing a smaller network, consisting of a dual-encoder network, which also resolves the instability issue that arises in the training process of large-scale visual models with the Swin Transformer, where activation values of residual units accumulate layer by layer, leading to a significant increase in differences in activation amplitudes across layers and causing model instability. The results of the experimental validation using real data show that our dual-encoder network has achieved significant performance improvements, and it also demonstrates a strong appeal in reducing computational complexity. [ABSTRACT FROM AUTHOR]

Rogue waves are sudden and extreme occurrences, with heights that exceed twice the significant wave height of their neighboring waves. The formation of rogue waves has been attributed to several possible mechanisms such as linear superposition of random waves, dispersive focusing, and modulational instability. Recently, nonlinear Fourier transforms (NFTs), which generalize the usual Fourier transform, have been leveraged to analyze oceanic rogue waves. Next to the usual linear Fourier modes, NFTs can additionally uncover nonlinear Fourier modes in time series that are usually hidden. However, so far only individual oceanic rogue waves have been analyzed using NFTs in the literature. Moreover, the completely different types of nonlinear Fourier modes have been observed in these studies. Exploiting twelve years of field measurement data from an ocean buoy, we apply the nonlinear Fourier transform (NFT) for the nonlinear Schrödinger equation (NLSE) (referred to NLSE-NFT) to a large dataset of measured rogue waves. While the NLSE-NFT has been used to analyze rogue waves before, this is the first time that it is systematically applied to a large real-world dataset of deep-water rogue waves. We categorize the measured rogue waves into four types based on the characteristics of the largest nonlinear mode: stable, small breather, large breather and (envelope) soliton. We find that all types can occur at a single site, and investigate which conditions are dominated by a single type at the measurement site. The one and two-dimensional Benjamin-Feir indices (BFIs) are employed to examine the four types of nonlinear spectra. Furthermore, we verify on a part of the data set that for the localized types, the largest nonlinear Fourier mode can be attributed directly to the rogue wave, and investigate the relation between the height of the rogue waves and that of the dominant nonlinear Fourier mode. While the dominant nonlinear Fourier mode in general only contributes a small fraction of the rogue wave, we find that soliton modes can contribute up to half of the rogue wave. Since the NLSE does not account for directional spreading, the classification is repeated for the first quartile with the lowest directional spreading for each type. Similar results are obtained. [ABSTRACT FROM AUTHOR]

In the human–robot collaboration system, the high-precision distortion correction of the camera as an important sensor is a crucial prerequisite for accomplishing the task. The traditional correction process is to calculate the lens distortion with the camera model parameters or separately from the camera model. However, in the optimization process calculate with the camera model parameters, the mutual compensation between the parameters may lead to numerical instability, and the existing distortion correction methods separated from the camera model are difficult to ensure the accuracy of the correction. To address this problem, this study proposes a model-independent lens distortion correction method based on the image center area from the perspective of the actual camera lens distortion principle. The proposed method is based on the idea that the structured image preserves its ratios through perspective transformation, and uses the local image information in the central area of the image to correct the overall image. The experiments are verified from two cases of low distortion and high distortion under simulation and actual experiments. The experimental results show that the accuracy and stability of this method are better than other methods in training and testing results. [ABSTRACT FROM AUTHOR]

In recent studies, it has been shown that under optimal dual pulse irradiation, it is possible to generate anomalous relativistic temperature (> 500 keV) electron emission even with mJ/pulse lasers at 1/100th of the relativistic intensity when micrometer droplets of methanol are used as a high repetition rate target. In this paper, we present the results of doping these droplets with CH3I to bring out a 30-fold enhancement in electron emission. Experiments and simulations presented here find a route to enhance electron emission driven by two plasmon decay instability. Improving compact laser plasma based sources of MeV electrons, x-ray emission schemes that use a high repetition rate, and mJ/pulse laser systems is important not only for basic science but also applications of imaging and radiography. [ABSTRACT FROM AUTHOR]

Multipulse laser–matter interactions initiate nonlinear and nonequilibrium plasma fluid flow dynamics and their instability creating microscale vortex filaments, loop-soliton chains, and helically paired structures, similar to those at the astrophysical mega scale. We show that the equation with the Hasimoto structure describes both, the creation of loop solitons by torsion of vortex filaments and the creation of solitons by helical winding of magnetic field lines in the Crab Nebula. Our experiments demonstrate that the breakup of the loop solitons creates vortex rings with (i) quasistatic toroidal Kelvin waves and (ii) parametric oscillatory modes—i.e., with the hierarchical instability order. For the first time, we show that the same hierarchical instability at the micro- and the megascale establishes the conceptual frame for their unique classification based on the hierarchical order of Bessel functions. Present findings reveal that conditions created in the laser-target regions of a high filament density lead to their collective behavior and formation of helically paired and filament-braided "complexes". We also show, for the first time, that morphological and topological characteristics of the filament-bundle "complexes" with the loop solitons indicate the analogy between similar laser-induced plasma instabilities and those of the Crab and Double-Helix Nebulas—thus enabling conceptualization of fundamental characteristics. These results reveal that the same rotating metric accommodates the complexity of the instabilities of helical filaments, vortex rings, and filament jets in the plasmatic micro- and megascale astrophysical objects. [ABSTRACT FROM AUTHOR]

Engineers need to know properties of shallow marine sediments to build piers, pipelines and even offshore windfarms. We present a method for estimating the density, P velocity and thickness of these sediments. The traveltime inversion of primary and multiple reflections enables their semiquantitative estimation in marine surveys when using a minimal acquisition system such as a monochannel Boomer. Picking errors, ambient noise and interfering events lead to significant errors in the estimates. Similar, albeit milder, instabilities occur when inverting the signal amplitudes to determine the reflectivity of the layer interfaces. In this paper, we introduce a coupling between the separate inversion of amplitudes and traveltimes to obtain a better Earth model. The P velocity shows up in two stable terms provided by the separate inversions: the acoustic impedance of shallow sediments (through the amplitudes) and the transit time across the sediment layer (through the traveltimes). We couple the two inversion engines by imposing a smoothness condition on velocity and density and thickness of the layer while keeping the impedance and traveltime constant. We thus exploit the ambiguity of the solution to introduce geological criteria and reduce the noise contribution. We validated the proposed method with synthetic and real data. [ABSTRACT FROM AUTHOR]

A deterministic system of ocean surface waves and flow in the oceanic boundary layer is key to understanding the dynamics of the upper ocean. For the description of such complex systems, a higher‐order shear‐current modified nonlinear Schrödinger equation is newly derived and then used to physically interpret the interplay between Stokes drift, Eulerian return flow due to a passing wave group, and an open‐ocean vertically sheared flow in the extreme sea wave generation. The conditions for the suppression or enhancement of the modulation instability in the rogue wave dynamics in the presence of a background flow are reported, whose relevance and influence to the Craik‐Leibovich type 2 instability in triggering a Langmuir‐type circulation is discussed. The findings highlight the need for future studies to establish and assess the energy transfer from waves to currents or in the reversing order, asserting a plausible physical mechanism for the dissipation of the surface wave energy through wave‐current interactions in the open ocean. Plain Language Summary: The dynamics of the upper‐ocean involve many complex processes, including for instance the interplay between wind, waves, currents, and global circulation systems. Such interactions can give rise to instabilities and extreme events with far‐reaching consequences. In this letter, we use a newly derived weakly nonlinear wave framework accounting for the presence of shear currents to quantify the requirements to trigger modulation instability, giving rise to long‐crested rogue waves. Our investigation also provides combined conditions for the occurrence of both, modulation and Craik‐Leibovich (type 2) instabilities, and demonstrates the possibility of energy transfers between waves as well as between waves and currents in the ocean. Key Points: An advanced shear‐current modified nonlinear Schrödinger‐type equation is derived for surface waves in a background open‐ocean flowThe interplay between Stokes drift, background flow, and Eulerian return flow by a wave group, in extreme waves generation is revealedHow a background flow suppresses the modulational instability is explained and its relevance to the CL2 instability is discussed [ABSTRACT FROM AUTHOR]

Two‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation. Plain Language Summary: Recent studies have unveiled the generation of nonlinear second harmonics (SH) of electromagnetic ion cyclotron (EMIC) waves. The SH is nonlinearly driven by the fundamental wave (FW) and satisfies the necessary conditions: ω2 = 2ω1 and k2 = 2k1, where ω1 (ω2) and k1 (k2) are the frequency and the wave vector of the FW (SH), respectively. Previous studies have relied on one‐dimensional (1‐D) hybrid simulations to investigate the SH. However, 1‐D simulations allow waves to propagate along a single dimension and lack spatial variation of the field orthogonal to this dimension, which impedes the complete verification of the relation k2//k1. Thus, in this study, the SH generation is modeled by two‐dimensional (2‐D) hybrid codes. The simulated SH exhibits characteristics similar to typical EMIC waves with left‐hand polarization and small wave normal angle. The bicoherence index is utilized to reveal the phase coupling between the SH and FW. The necessary conditions, especially for the wave vector relation, are verified from a 2‐D perspective for the first time. Additionally, the amplitude ratios of the SH to the FW and their phase velocities are compared with theoretical results. The comprehensive analyses of this study provide substantial evidence for the SH generation mechanism. Key Points: Two‐dimensional (2‐D) hybrid codes are developed to model the nonlinear second‐harmonic (SH) generation of electromagnetic ion cyclotron wavesThe necessary conditions required by the SH generation mechanism are verified from a 2‐D perspectiveThe theoretical amplitude ratios between harmonics are only satisfied in the SH saturation stage [ABSTRACT FROM AUTHOR]

The higher-order nonlinear Schrödinger equation with combined nonlinearities is derived by an asymptotic reduction from the (2+4) Korteweg–de Vries model for weakly nonlinear wave packets for the context of interfacial waves in a three-layer symmetric media. Focusing properties and modulation instability effects are discussed for the considered physical context. Instability growth rate, maximum of the increment and the boundaries of the instability interval are derived in terms of three-layer density stratification, their structure on the parameter planes of relative layer depth, carrier wavenumber and envelope amplitude, are considered in detail. [ABSTRACT FROM AUTHOR]

We consider a plasma model made of negative ions and electrons in Boltzmann distribution and cold mobile positive ions, under the influence of an external magnetic field, to study the propagation of ion-acoustic waves (IAWs). From the hydrodynamic equations of the two-dimensional (2D) electronegative plasma, the dynamics of the system is reduced via the reductive perturbation method to the Davey–Stewartson (DS) equations. Using the linear stability analysis of planar waves, an expression of the modulational instability growth rate is derived, and its response to system parameters, such as the negative ion concentration ratio, the electron-to-negative ion temperature ratio and the magnetic field is discussed. It comes out that the instability occurs for high values of the negative ion concentration ratio and in a very restrained area of small magnetic field values. The growth rate is maximum for high values of both the electron-to-negative ion temperature ratio and the magnetic field. The existence of IAWs in the model is confirmed. One-dromion and two-dromion solutions are investigated analytically using the Hirota’s bilinear method and numerically. The impact of the magnetic field is discussed in that context, and particular attention is given to dromion interactions under different scenarios. We noted a slowing effect on the propagation of the dromion solutions in the presence of the magnetic field. Elastic collision of two-dromion solutions is observed during their evolution, with an acceleration of the process in the presence of the magnetic field. [ABSTRACT FROM AUTHOR]

Ionospheric plasma introduces nonlinear perturbations in regular EM wave propagation which in turn affects the signal transmission in a highly nonlinear manner. Often the signals are distorted by a varied degree of nonlinearity. The wireless communication mechanism is affected by small perturbations which take gigantic rogue wave structures with the possibility of damaging sophisticated equipments. To study the evolution of rogue wave-type solitons starting from initial small-amplitude perturbations, we have considered a three-component electron–ion plasma system with degeneracy pressure as well as quantum diffraction effects. A solitary wave structure is formed due to the interplay of nonlinear and dispersive forces. Such a formation under an external force gets modified and the stability criteria are altered. The interesting fact thus obtained here shows that relativistic and thermal degeneracy favour stability whereas quantum diffraction leads to instability. In this paper, we have studied how solitary wave structures behave under an external force. Next, we study how the nonlinear effects cause an amplitude modulation and the envelope soliton is formed. Such an envelope soliton is studied by the nonlinear Schrödinger equation that we derive in the later part of the work. We have carried out simulation studies and compared our results with the analytical findings of other workers. [ABSTRACT FROM AUTHOR]

The present investigation focusses on studying the modulational instability of ion-acoustic waves in a multicomponent plasma system comprising positive ions, negative ions and electrons. The electron component is described by the κ -deformed Kaniadakis distribution, with the deformation parameter κ ranging from - 0.4 to 0.4. Using the standard perturbation method, the dispersion relation is derived from the governing equations. It is found that the dispersion relation is independent of κ but depends on other factors, such as the density ratio (α ), mass ratio (η ) and ion temperatures ( σ ± ). Two distinct ion-acoustic modes, namely the slow mode and the fast mode, are analysed in detail based on the phase velocity. The nonlinear Schrödinger equation is derived from the governing equations, whose dispersion and nonlinearity coefficients significantly impact the stability characteristics of ion-acoustic waves. Three plasma systems, namely H + H - , Ar + F - and H + O 2 - , which exist in the D-region of the atmosphere, are considered in this study. A comprehensive analysis is conducted for both slow and fast modes, taking into account the influence of the deformation parameter κ , mass ratios and ion temperatures. This investigation is relevant for understanding the behaviour of ion-acoustic waves in space and laboratory plasmas where multiple ion species coexist. [ABSTRACT FROM AUTHOR]

This paper focusses on a class of non-isospectral (2 + 1) -dimensional Calogero–Degasperis system, which is a more general form of the classical nonlinear Schrödinger equation. Primarily, according to the plane wave seed solutions, we analyse the modulational instability of this system and obtain the formation mechanism of different localised waves. Secondly, based on the known Lax pair, we construct the generalised (n , N - n) -fold Darboux transformation of this system. As an application of the resulting Darboux transformation, we not only show the interaction structures of the multisoliton solutions, but also analyse its long-time asymptotic behaviours and list the relevant physical properties. In order to explore the relationship with differential geometry, we also show the multisoliton surfaces. Subsequently, we give some higher-order lump solutions and analyse their large-parameter asymptotic states. We also give some mixed interactional solutions to better understand the interaction phenomena of different localised waves, whose propagation structures and characteristics are shown graphically. These results and phenomena may be helpful to understand some physical phenomena in nonlinear optics, fluids and Bose–Einstein condensates. [ABSTRACT FROM AUTHOR]

Optical Fabry–Perot cavity with a movable mirror is a paradigmatic optomechanical system. While usually the mirror is supported by a mechanical spring, it has been shown that it is possible to keep one of the mirrors in a stable equilibrium purely by optical levitation without any mechanical support. In this work, we expand previous studies of the nonlinear dynamics of such a system by demonstrating a possibility for mechanical parametric instability and the emergence of the "phonon laser" phenomenon. [ABSTRACT FROM AUTHOR]

Standard time-series modeling requires the stability of model parameters over time. The instability of model parameters is often caused by structural breaks, leading to the formation of nonlinear models. A state-dependent model (SDM) is a more general and flexible scheme in nonlinear modeling. On the other hand, time-series data often exhibit multiple frequency components, such as trends, seasonality, cycles, and noise. These frequency components can be optimized in forecasting using Singular Spectrum Analysis (SSA). Furthermore, the two most widely used approaches in SSA are Linear Recurrent Formula (SSAR) and Vector (SSAV). SSAV has better accuracy and robustness than SSAR, especially in handling structural breaks. Therefore, this research proposes modeling the SSAV coefficient with an SDM approach to take structural breaks called SDM-SSAV. SDM recursively updates the SSAV coefficient to adapt over time and between states using an Extended Kalman Filter (EKF). Empirical results with Indonesian Export data and simulation studies show that the accuracy of SDM-SSAV outperforms SSAR, SSAV, SDM-SSAR, hybrid ARIMA-LSTM, and VARI. [ABSTRACT FROM AUTHOR]

The rapid development of unmanned aerial vehicles (UAVs) provides a new application mode for gas remote sensing. Compared with fixed observation and vehicle-mounted platforms, a Fourier transform infrared spectrometer (FTIR) integrated in the UAV can monitor chemical gases across a large area, can collect data from multiple angles in three-dimensional space, and can operate in contaminated or hazardous environments. The unmanned helicopter has a larger payload and longer endurance than the rotary-wing drone, which relaxes the weight, size and power consumption limitations of the spectrometer. A FTIR remote sensing system integrated in an unmanned helicopter was developed. In order to solve the data acquisition and analysis problem caused by vibration and attitude instability of the unmanned helicopter, a dual-channel parallel oscillating mirror was designed to improve the stability of the interferometer module, and a robust principal component analysis algorithm based on kernel function was used to separate background spectrum and gas features. The flight experiment of sulfur hexafluoride gas detection was carried out. The results show that the system operates stably and can collect and identify the target spectrum in real time under the motion and hovering modes of an unmanned helicopter, which has broad application prospects. [ABSTRACT FROM AUTHOR]

The goal of this work was to use conformable fractional derivative sense to create some crucial solitary waves for two models of space–time fractional nonlinear Schrödinger equations. We use the unified solver approach to accomplish this goal in a fully unified way. This solution is robust, practical, dependable, and simple to use. The obtained solutions are extremely important for describing critical complicated phenomena in fractional quantum mechanics, optical fiber communications, and energy applications. Some simulations are provided to demonstrate the behavior of the obtained solutions when appropriate physical parameters are used. It was noted that by increasing the fractal factors, the nonlinear wave propagates with a changing phase and wave frequency. Our research may open up new possibilities for optical manipulation in practical applications. Finally, further fractional physical models can be solved using the suggested technique. [ABSTRACT FROM AUTHOR]

This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross–Pitaevskii (GP) equations with the Lee–Huang–Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole–dipole and quadrupole–quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic ( χ (2) ) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT -symmetric version, a system of DNLS equations for the spin–orbit-coupled (SOC) binary Bose–Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT -symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others. [ABSTRACT FROM AUTHOR]

The aim of the present study is to identify multiple soliton solutions to the nonlinear coupled Broer-Kaup-Kupershmidt (BKK) system, including beta, conformable, local-fractional, and M-truncated derivatives. The coupled Broer-Kaup-Kupershmidt system is employed for modelling nonlinear wave evolution in mathematical models of fluid dynamics, plasmic, optical, dispersive, and nonlinear long-gravity waves. The travelling wave solutions to the above model are found using the Unified and generalised Bernoulli sub-ODE techniques. By modifying certain parameter values, we may create bright soliton, squeezed bell-shaped wave, expanded v-shaped soliton, W-shaped wave, singular soliton, and periodic solutions. The four distinct kinds of derivatives are compared quite effectively using 2D line graphs. Also, contour plots and 3D graphics are given by using Mathematica 10. Lastly, any pair of propagating wave solutions has symmetrical geometrical forms. [ABSTRACT FROM AUTHOR]

Recently, kagome lattice materials have emerged as a new model material platform for discovering and engineering novel quantum phases of matter. In this work, we elucidate the driving mechanism of the 3 × 3 charge order in a newly discovered kagome metal ScV6Sn6. Through multimodal investigations combining angle-resolved photoemission spectroscopy, phonon dispersion calculations, and phase diagram study, we identify the central role of unstable planar Sn and Sc phonon modes, while the electronic instability and van Hove singularities originating from the V kagome lattice have a marginal influence. Our results highlight that the 3 × 3 charge order in ScV6Sn6 is fundamentally distinguished from the electronically driven 2 × 2 charge order in the canonical kagome system AV3Sb5, uncovering a new mechanism to induce symmetry-breaking phase transition in kagome lattice materials. [ABSTRACT FROM AUTHOR]

Surface polishing by laser remelting (SP-LRM) is a novel, versatile, high-speed, and low-cost advanced manufacturing technology for producing high-quality surface finishes. The process utilizes a high-power laser that delivers a large amount of instantaneous energy melting a superficial thin layer of material to a molten state. This allows the melt pool to flow driven by thermocapillary and surface tension forces. The target of the process is to melt, reallocate, and resolidify surface peaks into valleys in order to yield a low surface roughness (Sa). SP-LRM, complexity arises from instabilities occurring during laser-material interactions, resulting from non-linear thermodynamics, initial surface topography, overheating, abrupt changes in laser path trajectories involving acceleration and deceleration, and various other factors. These process instabilities significantly affect the attainment of a desired smooth final surface. Presently, the identification of anomalies resulting from a specific set of laser parameters in laser remelting (LRM) is performed offline by assessing the surface topography of LRM using optical profilometer and correlating it with surface non-uniformities that are indicative of process instabilities. This study streamlines the anomaly detection process and identifies the presence of irregularities using an unsupervised clustering machine learning (ML) technique, specifically K-means clustering. During the laser remelting (LRM) process, a high-speed near-infrared (NIR) camera captures relative thermal emission images, which are then classified into a minimum of three clusters using the K-means algorithm. These clusters correspond to positive and negative axial laser beam positions, indicating shifts in the laser spot on the image, and the stability states of laser-material interactions. Preliminary findings show promising results in the employment of artificial intelligence (AI) to enhance LRM as a conventional industrial technology for polishing and structuring tooling surfaces. [ABSTRACT FROM AUTHOR]

Surface nanostructures etch without chemicals; owing to this, their development is a crucial technical process. Surface nanohillocks may be created by irradiating yttrium iron garnet (YIG) with 30-MeV C60 cluster ions. The nanohillock creation mechanism is disputed. In this study, we propose that the formation mechanism is a plasma collective effect of charged particles that depends on localized rogue waves. Rogue waves will explain YIG surface nanohillock creation using a traditional hydrodynamic plasma model. Analytically solving hydrodynamic ion fluid equations and Maxwellian electron distributions yields a non-linear Schrodinger equation. Solving the latter gives us plausible rogue wave domains. Rogue waves concentrate charged ions from the surroundings into a small, confined zone, generating surface nanohillocks. The relevance of different plasma parameters is highlighted in the rogue wave profile. [ABSTRACT FROM AUTHOR]

In this paper, highly dispersive optical solitons are obtained with the perturbed complex Ginzburg--Landau equation, incorporating the Kerr law of nonlinearity, by the complete discriminant classification approach. A variety of solutions emerge from this scheme that include solitons, periodic solutions and doubly periodic solutions. The numerical sketches support the analytical findings. [ABSTRACT FROM AUTHOR]

This paper addresses Radhakrishnan--Kundu--Lakshmanan equation that arises in the study of soliton dynamics in optical fibers. The bifurcation analysis is carried out and the phase portraits are displayed. The complete discriminant analysis also leads to solitons and other solutions to the model. [ABSTRACT FROM AUTHOR]

Salix psammophila, classified under the Salicaceae family, is a deciduous, densely branched, and erect shrub. As a leading pioneer tree species in windbreak and sand stabilization, it has played a crucial role in combating desertification in northwestern China. However, different genetic sources of Salix psammophila exhibit significant variations in their effectiveness for windbreak and sand stabilization. Therefore, it is essential to establish a rapid and reliable method for identifying different Salix psammophila varieties. Visible and near-infrared (Vis-NIR) spectroscopy is currently a reliable non-destructive solution for origin traceability. This study introduced a novel feature selection strategy, called qualitative percentile weighted sampling (QPWS), based on the principle of the long tail effect for Vis-NIR spectroscopy. The core idea of QPWS combines weighted sampling and percentage wavelength selection to identify key wavelengths. By employing a multi-threaded parallel execution of multiple QPWS instances, we aimed to search for the optimal feature bands to address the instability issues that can arise during the feature selection process. To address the problem of reduced prediction performance in one-dimensional convolutional neural network (1D-CNN) models after feature selection, we have introduced convolutional autoencoders (CAEs) to reduce the dimensions of wavelengths that are discarded during feature selection. Subsequently, these reduced dimensions are fused with the selected wavelengths, thereby enhancing the model's performance. With our completed model, we selected outstanding models for model fusion and established a decision system for Salix psammophila. It is worth noting that all 1D-CNN models in this study were developed using Bayesian optimization methods. In comparison with principal component analysis (PCA) and full spectrum methods, QPWS exhibits superior predictive performance in the field of machine learning. In the realm of deep learning, the fusion of data combining QPWS with CAE demonstrated even greater potential with an improvement of average accuracy of approximately 2.13% when compared to QPWS alone and a 228% increase in operational speed compared to a model with full spectra. These results indicated that the combination of CAE with QPWS can be an effective tool for identifying the origin of Salix psammophila. [ABSTRACT FROM AUTHOR]

Future GRACE-like geodesy missions could benefit from adopting accelerometer technology akin to that of the LISA Pathfinder, which employed laser interferometric readout at the sub-picometer level in addition to the conventional capacitive sensing, which is at best at the level of 100 pm. Improving accelerometer performance holds great potential to enhance the scientific output of forthcoming missions, carrying invaluable implications for research in climate, water resource management, and disaster risk reduction. To reach sub-picometer displacement sensing precision in the millihertz range, laser interferometers rely on suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods are available with varying levels of complexity, size, and performance. In this paper, we describe the performance of a Mach–Zehnder interferometer based on a compact monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in 10 13 , corresponding to an interferometer pathlength stability better than 1 pm / Hz . The prism was designed to host a second interferometer to interrogate the position of a test mass. This optical scheme has been dubbed "single-element dual-interferometer" or SEDI. [ABSTRACT FROM AUTHOR]

Images captured from different viewpoints or devices have often exhibited significant geometric and photometric differences due to factors such as environmental variations, camera technology differences, and shooting conditions' instability. To address this problem, homography estimation has attracted much attention as a method to describe the geometric projection relationship between images. Researchers have proposed numerous homography estimation methods for single-source and multimodal images in the past decades. However, the comprehensive review and analysis of homography estimation methods, from feature-based to deep learning-based, is still lacking. Therefore, we provide a comprehensive overview of research advances in homography estimation methods. First, we provide a detailed introduction to homography estimation's core principles and matrix representations. Then, we review homography estimation methods for single-source and multimodal images, from feature-based to deep learning-based methods. Specifically, we analyze traditional and learning-based methods for feature-based homography estimation methods in detail. For deep learning-based homography estimation methods, we explore supervised, unsupervised, and other methods in-depth. Subsequently, we specifically review several metrics used to evaluate these methods. After that, we analyze the relevant applications of homography estimation and show the broad application prospects of this technique. Finally, we discuss current challenges and future research directions, providing a reference for computer vision researchers and engineers. [ABSTRACT FROM AUTHOR]

In this study, we investigated the effect of self-phase modulation (SPM)-induced modulation instability (MI) on the spectral purity of high-power narrow-linewidth fiber amplifiers and established a spectral evolution model for SPM-induced MI in those amplifiers. The spectral evolution process of MI under different laser powers was simulated and analyzed. The results show that, at low power (100 W), SPM can cause a dynamic change in the spectral sideband secondary peak and the spectral wingspan. An increase in laser power led to the cascade effect of MI, forming a zigzag secondary sideband with a larger spectral width and causing the spectral main peak and spectral broadening to split. Experiments based on the fiber Bragg grating (FBG) of oscillating seed sources were carried out on high-power narrow-linewidth laser amplifiers, and the above spectral evolution phenomenon was observed. The experimental results indicate that the spectral evolution model based on SPM-induced MI can effectively explain the dynamic change in the spectral secondary peak, spectral wingspan and zigzag broadening phenomenon in the power amplification process of narrow-linewidth lasers. [ABSTRACT FROM AUTHOR]

This study considers the generation and evolution of chirp-free soliton trains in a focusing cubic-quintic nonlinear optical fiber media (by utilizing experimental parameters), under the influence of weak nonlocal nonlinearity. Analysis of modulational instability (MI) reveals that the MI gain exist only in the anomalous dispersion regime, with the quintic nonlinear term increasing the maximum gain and sideband frequencies. The nonlocal nonlinearity parameter generally suppresses the impact of MI, because the maximum gain is greatly reduced with increase in nonlocality. By using the subsidiary ordinary differential equation method, stationary periodic soliton trains are obtained; with the intensity of the optical beam greatly reduced and frequency increased as nonlocality is gradually stepped up. However, an increase in nonlocality instead reduces the frequency of the traveling optical signals; derived via an efficient transformation method. Our results strongly suggest that nonlocal nonlinearity has potential applications in the control of laser beams; as nonlinear periodic optical signals can be easily transformed to very weak quasi-plane waves.

Surface nanostructures etch without chemicals; owing to this, their development is a crucial technical process. Surface nanohillocks may be created by irradiating yttrium iron garnet (YIG) with 30-MeV C60 cluster ions. The nanohillock creation mechanism is disputed. In this study, we propose that the formation mechanism is a plasma collective effect of charged particles that depends on localized rogue waves. Rogue waves will explain YIG surface nanohillock creation using a traditional hydrodynamic plasma model. Analytically solving hydrodynamic ion fluid equations and Maxwellian electron distributions yields a non-linear Schrödinger equation. Solving the latter gives us plausible rogue wave domains. Rogue waves concentrate charged ions from the surroundings into a small, confined zone, generating surface nanohillocks. The relevance of different plasma parameters is highlighted in the rogue wave profile.

We consider in this study the (3+1)-dimensional stochastic potential Yu–Toda–Sasa–Fukuyama with conformable derivative (SPYTSFE-CD) forced by white noise. For different kind of solutions of SPYTSFE-CD, including hyperbolic, rational, trigonometric and function, we use He's semi-inverse and improved (G ′ / G) -expansion methods. Because it investigates solitons and nonlinear waves in dispersive media, plasma physics and fluid dynamics, the potential Yu–Toda–Sasa–Fukuyama theory may explain many intriguing scientific phenomena. We provide numerous 2D and 3D figures to address how the white noise destroys the pattern formation of the solutions and stabilizes the solutions of SPYTSFE-CD. [ABSTRACT FROM AUTHOR]

This paper examines the propagation of M-shape solitons and their interactions with kink waves to the (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries (ISKdV) problem by applying the symbolic computation with ansatz functions technique and logarithmic transformation. The governing model usually appears in the nonlinear shallow water waves and fluid mechanics. We discuss various nonlinear waves like multiwave solutions (MSs), homoclinic breather (HB), M-shape solitons, single exponential form (one-kink), and double exponential form (two-kink). These waves have lot of applications in fluid dynamics, nonlinear optics, chemical reaction networks, biological systems, climate science, and material science. We also study interaction among M-shape solitons with kink wave. At the end, we discuss the stability characteristics of all solutions. [ABSTRACT FROM AUTHOR]

The presented work examines the stability of general rotors subject to harmonic follower force. The examined rotor consists of asymmetric Timoshenko shaft carrying asymmetric rigid disk and supported by anisotropic flexible bearings. The assumed modes method is combined with Lagrange's equation to derive the governing equations of motion with the help of symbolic computation. The employed approach resulted in equations of motion with multi-frequency periodic coefficients, and Floquet's method was used to determine stability boundaries of the considered rotors. After validation of the proposed mathematical model, it was employed to examine the combined effect of rotor asymmetry, support anisotropy, and rotor speed on its stability in the presence of harmonic follower force. The presented results show that the considered general rotor exhibits both subharmonic and combination instabilities, which were completely identified and investigated. Additional higher order subharmonic and combination instabilities are observed for general rotors only. [ABSTRACT FROM AUTHOR]

The paper aims to construct optical solitons and travelling wave solutions to two birefringent nonlinear models which consist of two-component form of vector solitons in optical fibre: the Biswas–Arshed model with Kerr-type nonlinearity and without four-wave mixing terms and the nonlinear Schrödinger equation with quadratic-cubic law of refractive index along with four-wave mixing terms. These nonlinear Schrödinger equations are applied in many physical and engineering fields. Optical solitons are considered in the context of photonic crystal fibres, couplers, polarisation-preserving fibres, metamaterials, birefringent fibres, and so on. Two reliable integration architectures, namely, the extended simplest equation method and the generalised sub-ODE approach, are adopted. As a result, bright soliton, kink and dark soliton, singular soliton, hyperbolic wave, a periodic wave, elliptic function solutions of Weierstrass and Jacobian types, and other travelling wave solutions, such as breather solutions and optical rogons, are derived, together with the existence conditions. In addition, the amplitude and intensity diagrams are portrayed by taking appropriate values for a few selected solutions. Furthermore, based on linear stability analysis, the modulation instability was explored for the obtained steady-state solutions. The reported results of this paper can enrich the dynamical behaviours of the two considered nonlinear models and can be useful in many scientific fields, such as mathematical physics, mathematical biology, telecommunications, engineering and optical fibres. This study confirms that the proposed approaches are sufficiently effective in extracting a variety of analytical solutions to other nonlinear models in both engineering and science. [ABSTRACT FROM AUTHOR]