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We propose a comprehensive analysis of the modulational instability (MI) phenomenon in one-dimensional Bose-Einstein condensate (BEC) in the context of mutually symmetric components in the binary mixture. The proposed model considers weak nonlocal cubic mean-field and quadratic beyond mean-field interactions arising from quantum fluctuations. The instability regions are analyzed using linear stability analysis of a continuous wave, considering maximum perturbation wavenumber and growth rate. The regions for quantum droplets (QDs) and solitons are identified by varying the nonlocality parameter. Numerical simulations confirm analytical predictions, revealing that nonlocality influences the formation of various QD profiles and instability time. Furthermore, solitonic patterns exhibit nonlocality-dependent behavior. Our study opens new doors to a better characterization of QDs in binary mixtures in the presence of higher-order beyond mean-field effects. • Wave instability is studied in Bose-Einstein condensate with weak nonlocal two-body interactions and nonlocal quantum fluctuations. • Regions for quantum droplets and solitons are identified by varying the nonlocality parameter. • Nonlocality influences the formation of various quantum droplet profiles and impacts the instability time. • Solitonic patterns exhibit nonlocality-dependent behaviors. [ABSTRACT FROM AUTHOR]

• Comparative analysis between the experimental observations and the numerical simulations, conducted using the high-order nonlinear Schrödinger equation (HNLSE). • The numerical outcomes demonstrated a high degree of consistency with the experimental data. • The results of these simulations suggested that as water depth transitions from shallow to deeper conditions, the wave height amplification factor diminishes. The evolution of the Peregrine breather (PB) in a wave tank is experimentally studied under water depths k 0 h (where k 0 represents the wave number and h the water depth) ranging from 4.35 to 5.24. Additionally, the initial wave steepness, ε 0 = k 0 a 0 (with a 0 being the background wave amplitude), was varied within the range of 0.077 to 0.116. Comparative analysis between the experimental observations and the numerical simulations, conducted using the high-order nonlinear Schrödinger equation (HNLSE), revealed that the HNLSE proficiently captures intricate details of wave field evolution, including a pronounced left–right asymmetry in surface elevations. The numerical outcomes demonstrated a high degree of consistency with the experimental data. Furthermore, numerical methodologies were employed to examine the fluctuation of wave height relative to water depth. The results of these simulations suggested that as water depth transitions from shallow to deeper conditions, the wave height amplification factor diminishes, eventually stabilizing. This implies that under shallower water conditions, there is a propensity for larger wave generation. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the dynamical behavior and modulation instability of optical solitons with spatio-temporal dispersion for the variable-coefficient nonlinear Schrödinger equation. The expressions of one-soliton solutions are derived, and the dynamical behaviors of one-soliton are studied by selecting the appropriate coefficient functions. Some interesting motion trajectories of solitons under the influence of variable-coefficient functions are revealed. In addition, the distribution of modulation instability (MI) gain versus the power, time and wave number is studied based on the linear stability analysis. The effect of the spatio-temporal dispersion on soliton transmission and gain is characterized. The obtained results are visualized in the 3D space by MATLAB or MAPLE. The results obtained in this paper provide a significant contribution to the formation of optical solitons in nonlinear optical fiber systems or other physical problems. • Based on variable-coefficient nonlinear Schrödinger equation, the dynamical behavior and modulation instability of optical solitons with spatio-temporal dispersion is investigated. • Based on the linear stability analysis, the distribution of modulation instability gain is studied. • The effect of the spatio-temporal dispersion on soliton transmission and gain is characterized, which paves the way for the study of optical spatio-temporal system. [ABSTRACT FROM AUTHOR]

We consider coupled dimensionless Gross-Pitaevskii (GP) equations that describes effective coherently coupled Bose–Einstein condensates (BECs) trapped in external complex potentials. Through a modified similarity transformation, the integrability condition is obtained and the system is reduced to one single integrable autonomous cubic-quintic nonlinear Schrödinger (NLS) equation with self-steepening and self-frequency shift. The baseband modulational instability (MI) for the obtained NLS equation is investigated in details. Through the exact first- and second-order rogue wave solutions with nonlinear chirp of the coupled GP equation, we investigate analytically the propagation dynamics of rogue waves on weakly perturbed continuous wave solutions in the parameter space where the baseband MI exist. Our results show that one can manipulate the motion of matter rogue waves by controlling the external trapping potential. Simulations provide supporting evidence that rogue waves can only emerge in regimes where baseband MI occurs. Our results show how multiplet first- and second-order rogue waves can be generated by varying some solution parameters such as the amplitude parameter. • A coupled Gross-Pitaevskii equations for a coherently coupled Bose-Einstein condensates are considered. • The integrability condition is obtained and the system is reduced into a single autonomous nonlinear Schrödinger equation. • Baseband modulational instability for the derived nonlinear Schrödinger equation is investigated. • Rational solutions with nonlinear chirp are constructed. • The dynamics of first- and second-order chirped rogue waves for coherently coupled Bose-Einstein condensates is studied. [ABSTRACT FROM AUTHOR]

This letter studies the excitation of nonlinear patterns on the one-dimensional (1D) quantum droplet in the presence of polaron-like impurity under modulational instability (MI) activation. Analytically, it is shown that strong coupling between the impurity and Bose species expands the instability domain, especially in the quantum droplet regime, while pronounced self-repulsive nonlinearity tends to restrict the MI to regions of strong interspecies interactions. In the process, the wavenumber spectrum, capable of supporting MI, also shrinks. Direct numerical simulations confirm the existence of coupled boson-impurity wave patterns, mainly governed by trains of solitary waves of different profiles for the impurity and quasi-droplet waveforms for the boson. Additionally, the two components are mutually trapped, which enhances energy transfer between them, leading to the formation of quasi-droplet structures under a suitable balance between the back action of the impurity on the boson, the Lee-Huang-Yang term, as well as the intrinsic self-repulsive nonlinearity. • One-dimensional quantum droplets in the presence of polaronic impurity are studied. • Strong coupling between the impurity and Bose species expands the instability domain in the quantum droplet regime. • Modulational instability is restricted to regions of strong interspecies interactions under self-repulsive nonlinearity. • Coupled boson-impurity wave patterns are governed by trains of solitary waves and quasi-droplet waveforms. [ABSTRACT FROM AUTHOR]

The letter proposes a modified set of coupled two-dimensional (2D) cubic complex Ginzburg-Landau (CGL) equations that include Rashba and Dresselhaus as well as helicoidal spin-orbit couplings (SOCs) and further study matter-wave formation using modulational instability (MI) in 2D Bose-Einstein condensates (BECs). Analytically, the linear stability analysis proposes an expression for the MI gain. The subsequent parametric study explores the effects of the included SO coupling, principally the competition involving the Rashba-Dresselhaus (RD) SOCs and the helicoidal SOC. Numerically, analytical predictions are confirmed through the emergence of dissipative nonlinear patterns under a suitable balance of the competing SOC terms, manifested by the disintegration of the continuous waves in a broad range of structures under effective energy exchange between the two BEC components. Combining dissipative effects and SOC in a 2D context extends the class of physical models that can investigate various suitable wave patterns in binary BECs. • Matter-wave formation using modulational instability in 2D dissipative open Bose-Einstein condensates is studied. • The presence of competing Rashba, Dresselhaus, and helicoidal spin-orbit couplings impacts the distribution of parameter domains. • The interplay between the spin-orbit coupling gives rise to dissipative solitons through direct numerical simulations. • New wave patterns are induced by the annihilation/recombination process as part of energy exchange between the two BEC species. [ABSTRACT FROM AUTHOR]

We investigate the discrete nonlinear Schrödinger model with helicoidal hopping and a power-law nonlinearity, motivated by the tunable nonlinearity in the model of DNA chain and ultra-cold atoms trapped in a helix-shaped optical trap. In the study of modulational instability, we find a successive destabilization along with increasing nonlinear-power. In particular, the critical amplitudes of second-stage instability decrease as nonlinear-power increases. Furthermore, it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. This link enable us to analytically estimate the critical parameters at which the breather solutions turn unstable, and find these parameters are dramatically influenced by the nonlinear-power. The stability properties of localized breathers perform an obvious change when the nonlinear power crosses a critical value γ c r . It is reflected that at weak nonlinearity the breathers exhibit monostability, while exceeding γ c r the bistability and instability will set in. The interplay between nonlinear-power and long-range hopping on the stability properties of breathers is also discussed in detail. [ABSTRACT FROM AUTHOR]

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov–Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission. [ABSTRACT FROM AUTHOR]

The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations. [ABSTRACT FROM AUTHOR]

The effect of two- and three-body interactions on the modulation instability (MI) domain formation of a spin-orbit (SO) and Rabi-coupled Bose-Einstein condensate is studied within a quasi-one-dimensional model. To this aim, we perform numerical and analytical investigations of the associated dispersion relations derived from the corresponding coupled Gross-Pitaevskii equation. The interplay between the linear (SO and Rabi) couplings with the nonlinear cubic-quintic interactions are explored in the mixture, considering miscible and immiscible configurations, with a focus on the impact in the analysis of experimental realizations with general binary coupled systems, in which nonlinear interactions can be widely varied together with linear couplings. • Modulation instability of Spin-orbit coupled Bose-Einstein condensates. • Interplay between linear with two- and three-body nonlinear interactions. • Dispersion relations by linear stability analysis. • Miscible and immiscible configurations. [ABSTRACT FROM AUTHOR]

Modulational instability (MI) is addressed in an optical fiber under competing effects between pure-quartic dispersion (PQD), self-steepening, and intrapulse Raman response. The self-steepening parameter reduces the maximum MI gain and the frequency bandwidth. Under the combined effects of the self-steepening and intrapulse Raman scattering, more spectral windows appear in the gain spectrum, induced by the increasing Raman effect. Numerical results fully concur with the theoretical predictions. The MI is manifested by the emergence of ultrashort pulses trains and rogue wave breathing trains. Under increasing self-steepening effect, asymmetric sidebands, reversible via the Raman scattering effect, appear in the spectral and temporal evolution of the pulse trains, which probes the tunability of energy transfer between the mode during signal propagation. Our results open up further perspectives for exploring mechanisms to generate ultrashort pulses in PQD optical media under higher-order nonlinearities, with applications to silicon photonic crystal waveguides and silica photonic crystal fibers. • Modulational instability in an optical fiber is studied under competing effects between pure-quartic dispersion, self-steepening, and intrapulse Raman response. • The self-steepening parameter reduces the maximum MI gain and the frequency bandwidth. • Additional spectral windows emerge in the gain spectrum, induced by the increasing Raman effect. • The emergence of ultrashort pulses trains and rogue wave breathing trains manifests the MI. [ABSTRACT FROM AUTHOR]

We study the spatiotemporal formation of patterns in a diffusive FitzHugh–Nagumo network where the effect of electromagnetic induction has been introduced in the standard mathematical model by using magnetic flux, and the modulation of magnetic flux on membrane potential is realized by using memristor coupling. We use the multi-scale expansion to show that the system equations can be reduced to a single differential-difference nonlinear equation. The linear stability analysis is performed and discussed with emphasis on the impact of magnetic flux. It is observed that the effect of memristor coupling importantly modifies the features of modulational instability. Our analytical results are supported by the numerical experiments, which reveal that the improved model can lead to nonlinear quasi-periodic spatiotemporal patterns with some features of synchronization. It is observed also the generation of pulses and rhythmics behaviors like breathing or swimming which are important in brain researches. [ABSTRACT FROM AUTHOR]

Progress is reported on the modulational instability (MI) of ion-acoustic waves (IAWs) and dissipative rogue waves (RWs) in ultracold neutral plasmas (UNPs). The UNPs consist of inertial ions fluid and Maxwellian inertialess hot electrons, and the presence of an ion kinematic viscosity is allowed. For this purpose, a modified nonlinear Schrödinger equation (NLSE) is derived and then solved analytically to show the occurrence of MI. It is found that the (in)stability regions of the wavepacks are dependent on time due to of the existence of the dissipative term. The existing regions of the MI of the IAWs are inventoried precisely. After that, we use a suitable transformation to convert the modified NLSE into the normal NLSE whose analytical solutions for rogue waves are known. The rogue wave propagation condition and its behavior are discussed. The impact of the relevant physical parameters on the profile of the RWs is examined. [ABSTRACT FROM AUTHOR]

By means of linear stability analysis (LSA) and direct numerical simulations of the coupled Gross-Pitaevskii (GP) equations, we address the impurity induced modulational instability (MI) and the associated nonlinear dynamics in Bose-Einstein condensates (BECs). We explore the dual role played by the impurities within the BECs—the instigation of MI and the dissipation of the initially generated solitary waves. Because of the impurities, the repulsive BECs are even modulationally unstable and this tendency towards MI increases with increasing impurity fraction and superfluid-impurity coupling strength. However, the tendency of a given BEC towards the MI decreases with the decreasing mass of the impurity atoms while the sign of the superfluid-impurity interaction plays no role. The above results are true even for attractive BECs except for a weak superfluid-impurity coupling, where the MI phenomenon is marginally suppressed by the presence of impurities. The dissipation of the solitons reduces their lifetime and is eminent for a larger impurity fraction and strong superfluid-impurity strength respectively. • Modulational instability in a BEC coupled to a reservoir of Bose-condensed impurities is studied. • The presence of impurities in repulsive BECs makes them always modulationally unstable. • The tendency of a BEC towards MI increases with the increasing fraction of impurities. • The tendency of a BEC towards MI decreases with decreasing mass of impurities. • The dissipation in the generated solitons increases with the impurity fraction and superfluid-impurity coupling. [ABSTRACT FROM AUTHOR]

We introduce off-diagonal effects in the three-stranded model of α -helix chains, which bring about additional nonlinear terms to enhance the way energy spreads among the coupled spines. This is analyzed through the modulational instability theory. The linear stability analysis of plane wave solutions is performed and the competitive effects of diagonal and off-diagonal interactions are studied, followed by direct numerical simulations. Some features of the obtained solitonic structures are discussed. [ABSTRACT FROM AUTHOR]

We derive and study a general rational solution of a coupled defocusing Hirota equation which can be used to describe evolution of light in a two-mode fiber with defocusing Kerr effect and some certain high-order effects. We find some new excitation patterns in the model, such as M-shaped soliton, W-shaped soliton, anti-eye-shaped rogue wave and four-petaled flower rogue wave. The results are compared with the solutions obtained in other coupled systems like vector nonlinear Schrödinger equation, coupled focusing Hirota and Sasa–Satsuma equations. We explain the new characters by modulational instability properties. This further indicates that rational solution does not necessarily correspond to rogue wave excitation dynamics and the quantitative relation between nonlinear excitations and modulational instability should exist. [ABSTRACT FROM AUTHOR]

The influence of next-nearest-neighbor interactions (next-NNI) of dipole–dipole type is analyzed in Davydov model with saturable nonlinearities. We analytically study the regions of discrete modulational instability (MI) of plane carrier waves and it appears that this region decreases as the number of nearest neighbors, m , increases. We also show via the instability growth rate (gain) that when m increases, bandwidth of instability decreases. Otherwise, it is noted that the saturation also has an antagonistic effect on the gain. Numerical simulations indicate that the presence of next-NNI induced downward corrections of the time of onset of MI. After having sought Discrete Soliton (DS) and Discrete Multihump soliton (DMHS) numerically with m = 1 ; 2; 3, the next-nearest neighbor dependence of the width and height of these solutions is discussed. A study of mobility is achieved and it results that next-NNI increase the speed of DMHS. Furthermore, the collisions of two DMHS are performed and it emerges mainly that next-NNI lead to the formation of large stationary solitons. [ABSTRACT FROM AUTHOR]

We examine the cross-phase modulational instability in a two-core birefringent coupler made of a positive and negative index material. The modified form of generalized nonlinear Schrödinger equation contains a nonlinear septic term, cross-phase modulation, intrapulse Raman scattering, self-steepening, and conventional type of saturation nonlinearity. We investigate normal and anomalous group-velocity dispersion regimes and cases of birefringent effects such as zero-birefringence, linear birefringence, and circular birefringence. We observe that the MI gain spectrum shows significant changes in the presence of cross-phase modulation with a nonlinear saturation effect and non-Kerr nonlinearity. In addition, the self-steepening brings out new sidebands and shifts the existing sidebands to bring them together, providing a new pathway to generate solitons or ultrashort pulses in the presence of nonlinear septic saturation. The intrapulse Raman scattering effect causes conventional and Raman bands, extending the modulational instability (MI) domain range. The saturable nonlinearity suppresses the MI gain and reduces the bandwidth of the spectrum for both normal and anomalous dispersion regimes. But, in the case of nonlinear saturation with non-Kerr nonlinearity, the MI gain spectra exhibit efficient modification in a two-core birefringent oppositely directed coupler (ODCs) with adjustable effects of SS, IRS, and cross-phase modulation. Therefore, manipulating MI and solitons in a two-core ODCs is better performed when the birefringence is linear rather than circular. Here we present how to control and generate the MI and solitons in birefringent ODCs, emphasizing the negative index material (NIM) channel. • The role of septic saturation on modulational instability in two-core oppositely directed birefringent coupler is reported. • The cross-phase and nonlinear saturation can significantly change the MI gain spectrum. • The modulational instability gain is dominated by intra-pulse Raman scattering. • The gain spectrum non-monotonically changes with septic saturation α. • SS effect can generate new path to manipulate ultrashort pulse and soliton. [ABSTRACT FROM AUTHOR]

The modulational instability (MI) process is exclusively studied in a two-component Bose-Einstein condensate (BEC) which includes Rashba-Dresselhaus (RD) spin-orbit (SO) and helicoidal SO couplings. A generalized set of two-dimensional (2D) Gross-Pitaevskii (GP) equations is derived. The tunability of the helicoidal gauge potential is exploited to address BECs dynamics in a square lattice. The MI growth rate is derived, and parametric analyses of MI show the dependence of the instability on interatomic interaction strengths, the RD SO coupling, and helicoidal SO coupling, which combines the gauge amplitude and the helicoidal gauge potential. Direct numerical simulations are carried out to confirm the analytical predictions. Trains of solitons are obtained, and their behaviors are debated when the RD SO parameters are varied under different combinations between the gauge amplitude and the helicoidal gauge potential. The latter gives a potential way to manipulate the trapping capacities of the proposed BEC model. • A vector 2D Gross-Pitaevskii model with Rashba-Dresselhaus and helicoidal spin-orbit couplings is derived. • The tunability of the helicoidal gauge potential allows us to study dynamics in free space and a square lattice. • The modulational instability growth rate is derived and discussed for each case. • Direct numerical simulations confirm the existence of trains of solitons due to different combinations of the spin-orbit couplings. [ABSTRACT FROM AUTHOR]

We have considered the nonlinear propagation of an extraordinary electromagnetic wave in a transversely magnetized plasma. It is found that, in a weakly relativistic regime, evolution of the amplitude of an extraordinary wave packet is governed by a nonlinear Schrödinger (NLS) equation. The modulational instability of an extraordinary plane wave is investigated. The analytical solutions of the NLS equation in the forms of envelope solitons and rogue waves are reviewed and dependence of their structural properties on relevant parameters of the system is addressed. [ABSTRACT FROM AUTHOR]

We explain how the modulational and oscillatory instabilities can be generated in Bose–Einstein condensates (BECs) with two- and three-body interactions trapped in a periodic optical lattice with driving harmonic potential. We solve a cubic–quintic Gross–Pitaevskii (GP) equation with external trapping potentials by using both analytical and numerical methods. Using the time-dependent variational approach, we derive and analyze the variational equations for the time evolution of the amplitude and phase of modulational perturbation, and effective potential of the system. Through the effective potential, we obtain the modulational instability condition of the BECs with two- and three-body interactions and shown the effects of the optical potential on the dynamics of the system. We perform direct numerical simulations to support our analytical results, and good agreement is observed. [ABSTRACT FROM AUTHOR]

• Open two-dimensional two-component Bose-Einstein condensates are studied. • Rashba-Dresselhaus spin-orbit coupling and the Lee-Huang-Yang term are included. • Matter waves are investigated theoretically and numerically via modulational instability. • Numerical simulations give rise to vortex-like structures and more sophisticated soliton-molecules. • The spin-orbit coupling may be a valuable tool to predict and monitor modulational instability collapse. The modulational instability (MI) of continuous waves is exclusively addressed theoretically and numerically in a two-component Bose-Einstein condensate in the presence of a mixture of Rashba and Dresselhaus (RD) spin-orbit couplings and the Lee-Huang-Yang (LHY) term. The linear stability analysis is utilized to derive an expression for the MI growth rate. It is revealed that instability can be excited in the presence of the RD spin-orbit coupling under conditions where nonlinear and dispersive effects are suitably balanced. Analytical predictions are confirmed via direct numerical simulations, where MI is manifested by the emergence of soliton-molecules that include four-peaked solitons and more exotic vortex structures that are very sensitive to variations in spin-orbit coupling strengths. Our study suggests that MI is a suitable mechanism for generating matter waves through multi-peaked solitons of various geometries. [ABSTRACT FROM AUTHOR]

We consider the wind-forced nonlinear Schrödinger (NLS) equation obtained in the potential flow framework when the Miles growth rate is of the order of the wave steepness. In this case, the form of the wind-forcing terms gives rise to the enhancement of the modulational instability and to a band of positive gain with infinite width. This regime is characterised by the fact that the ratio between wave momentum and norm is not a constant of motion, in contrast to what happens in the standard case where the Miles growth rate is of the order of the steepness squared. [ABSTRACT FROM AUTHOR]

In this work we study the modulational instability of plasmas with q -entropy electrons and warm ions, using the hydrodynamic approach. A nonlinear Schrödinger equation (NLSE), governing the dynamics of envelope excitations in the plasma, is obtained by using the conventional multiscales method. Investigation of the modulational instability of the nonextensive plasmas reveals that the criteria for propagation of bright/dark envelope excitations in such plasmas are significantly affected by value of the nonextensivity parameter, q , and the fractional ion-temperature, σ . In particular, by setting σ ≠ 0 , a new region of modulational instability appears, indicating that the study of modulation instability in the cold-ion limit ( σ = 0 ) is completely different from that of warm ions. The study of the growth-rate and rogue-wave amplitudes in terms of different plasma parameters, reveals that their magnitude is of different scales for two ranges of the nonextensivity parameters, q > 1 and q < 1 . [ABSTRACT FROM AUTHOR]

The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation is that it provides a more faithful description of short waves of small amplitude. Recently, Ehrnström and Kalisch [19] established that the Whitham equation admits periodic traveling-wave solutions. The focus of this work is the stability of these solutions. The numerical results presented here suggest that all large-amplitude solutions are unstable, while small-amplitude solutions with large enough wavelength L are stable. Additionally, periodic solutions with wavelength smaller than a certain cut-off period always exhibit modulational instability. The cut-off wavelength is characterized by k[sub h0] = 1.145, where k = 2π/L is the wave number and [sub h0] is the mean fluid depth. [ABSTRACT FROM AUTHOR]

The propagation of finite amplitude ultra-low-frequency shear dust Alfvén (SDA) waves, and their modulational instability in a magnetized plasma medium of positive and negatively charged dust fluids have been theoretically investigated by using the reductive perturbation method. The derivative nonlinear Schrödinger equation is derived to examine the stability analysis of such SDA waves. It is found that the SDA waves propagating in such an opposite polarity dust plasma medium are modulationally unstable, and that the instability criterion and the growth rate of these unstable SDA waves in such a novel opposite polarity dust plasma medium are found to be significantly different from those in electron–ion or electron–positron plasma media. The implications of the present investigation in different space environments and laboratory devices are briefly discussed. [ABSTRACT FROM AUTHOR]

Abstract: Based on the wave equation of ultra-intense linearly polarized laser pulse propagating in electron–positron plasmas, the modulational instability is investigated. The nonlinear dispersion relation and the growth rate of instability are derived. The effects of plasmas number density, temperature, and laser intensity on the growth rate are analyzed. Results show that in an electron–positron plasma with certain background density, the intensity of the modulation instability is mainly determined by the competition between the nonlinearity in the interaction and the relativistic light ponderomotive driven density responses. [Copyright &y& Elsevier]

Abstract: We use the time-dependent variational approach to demonstrate how the modulational and oscillatory instabilities can be generated in Bose–Einstein condensates (BECs) trapped in a periodic optical lattice with weak driving harmonic potential. We derive and analyze the ordinary differential equations for the time evolution of the amplitude and phase of the modulational perturbation, and obtain the instability condition of the condensates through the effective potential. The effect of the optical potential on the dynamics of the BECs is shown. We perform direct numerical simulations to support our theoretical findings, and good agreement is found. [Copyright &y& Elsevier]

Abstract: Through a Gross–Pitaevskii equation comprising cubic, quartic, residual, and quintic nonlinearities, we examine the modulational instability (MI) of Bose–Einstein condensates at higher densities in the presence of quantum fluctuations. We obtain an explicit time-dependent criteria for the MI and the instability domains of the condensates. Solitons are generated by suitably exciting the MI, and their stability is analyzed. We find that quantum fluctuations can completely change the instability of condensates by reversing the nature of the effective two-body interactions. The interplay between three-body interactions and quantum fluctuations is shown. Numerical simulations performed agree with analytical predictions. [Copyright &y& Elsevier]

Abstract: We consider the amplitude modulation of low-frequency, long wavelength electrostatic drift wave packets in a nonuniform magnetoplasma with the effects of equilibrium density, electron temperature and magnetic field inhomogeneities. The dynamics of the modulated drift wave packet is governed by a nonlinear Schrödinger equation. The latter is used to study the modulational instability of a Stokeʼs wave train to a small longitudinal perturbation. It is shown that the drift wave packet is stable (unstable) against the modulation when the drift wave number lies in (). Thus, the modulated drift wave packet can propagate in the form of bright and dark envelope solitons or as a drift wave rogon. [Copyright &y& Elsevier]

Abstract: The nonlinear generation of shear field and flow in whistler waves is considered. It is shown that a coherent parametric process leads to modulational instability of four waves whistler interaction. Growth rates for the flow/field are compared with published simulation results. [Copyright &y& Elsevier]

Abstract: The amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, hot nonextensive q-distributed electrons, and stationary ions is presented theoretically. The nonlinear Schrödinger equation (NLSE) which governs the modulational instability of the EAWs is obtained using reductive perturbation method (RPM). The presence of the hot nonextensive q-distributed electrons is shown to influence the modulational instability of the waves. Further, the nondimensional parameter , which is the equilibrium density ratio of the hot to cold electron component, is shown to play a vital role in the formation of both bright and dark solitons. [Copyright &y& Elsevier]

Abstract: Modulation instability is investigated in two cubic–quintic Ginzburg–Landau equations coupled with a cross phase modulation type term. After carrying out a stability analysis an expression for gain is obtained. Some direct simulations to see the evolution of different continuous wave states are reported. These show the formation of modulation instability pulses as well as transitions from lower amplitude continuous wave states to higher amplitude continuous wave states. [Copyright &y& Elsevier]

Abstract: A multiple scales technique is employed to solve the fluid-Maxwell equations describing a weakly nonlinear circularly polarized electromagnetic pulse in magnetized plasma. A nonlinear Schrödinger-type (NLS) equation is shown to govern the amplitude of the vector potential. The conditions for modulational instability and for the existence of various types of localized envelope modes are investigated in terms of relevant parameters. Right-hand circularly polarized (RCP) waves are shown to be modulationally unstable regardless of the value of the ambient magnetic field and propagate as bright-type solitons. The same is true for left-hand circularly polarized (LCP) waves in a weakly to moderately magnetized plasma. In other parameter regions, LCP waves are stable in strongly magnetized plasmas and may propagate as dark-type solitons (electric field holes). The evolution of envelope solitons is analyzed numerically, and it is shown that solitons propagate in magnetized plasma without any essential change in amplitude and shape. [Copyright &y& Elsevier]

Abstract: We study the dynamical scattering in one-dimensional systems with a nonlinear side-coupled defect. Such structures exhibit the nonlinear Fano resonances, where nothing can propagate through. We developed a numerical model to study dynamical scattering. According to our analysis the scattering waves become dynamically unstable in the vicinity of the nonlinear Fano resonances, due to modulational instability caused by the presence of nonlinearity. It results in a time-growing amplitude of the nonlinear defect. We also demonstrate the existence of the nonlinear quasi-localized state, supported by such structures. [Copyright &y& Elsevier]

Abstract: The modulational instability of a plane wave for a discrete nonlinear Schrödinger equation with arbitrary nonlocality is analyzed. This model describes light propagation in a thin film planar waveguide arrays of nematic liquid crystals subjected to a periodic transverse modulation by a low frequency electric field. It is shown that nonlocality can both suppress and promote the growth rate and bandwidth of instability, depending on the type of a response function of a discrete medium. A solitary wave (breather-like) solution is built by the variational approximation and its stability is demonstrated. [Copyright &y& Elsevier]

• The phenomenon of MI induced by TOD using the CW solution is studied. • The system includes spatial dispersion accounting for Wannier exciton mass. • Such TOD tends to cause a broad MI spectrum at Stokes frequency. • The study also predicts the existence of Akhmediev type breathers and Peregrine rogue waves created by the TOD. It is well-known that third-order dispersion (TOD) plays no role in the onset of modulation instability in the nonlinear Schrödinger (NLS) family of systems. Here we demonstrate that the characteristics of modulational instability can be dramatically altered by the TOD in two different nonlinear systems, namely Wannier exciton mass in a ZnCdSe/ZnSe semiconductor superlattice and nonlinear pulse/beam propagation in a Kerr-like waveguide under non-slowly varying envelope approximation (non-SVEA), with spatial dispersion. Further we reveal the results of numerical simulations suggesting the existence of recently much studied Akhmediev-type breathers and Peregrine-like rogue waves due to the nonlinear development of MI stemming from the TOD. [ABSTRACT FROM AUTHOR]

• Coupled discrete GP equation with SOC is solved by linear stability analysis. • We address the impact of SOC on the MI of two-component discrete BECs. • SOC allows us to produce the MI even for a small wavenumber in miscible states. • In particular, SOC introduces MI even in the absence of hopping coefficient. • We have also corroborated the results of linear stability analysis numerically. We address the impact of intra-site spin-orbit (SO) coupling and associated inter-component Rabi coupling on the modulational instability (MI) of plane-wave states in two-component discrete Bose-Einstein condensates (BECs). Conditions for the onset of the MI and the respective instability are found analytically. SO coupling allows us to produce the MI even for a small initial wavenumber (q < π / 2) for miscible states. In particular, SO coupling introduces MI even in the absence of hopping coefficient, a concept which may have wider ramifications in heavy atomic BECs. We have also shown how our results of the linear stability analysis can be corroborated numerically. The fact that we have brought out the stability criteria in different domains of system parameters means that our model is tailor made experiments. [ABSTRACT FROM AUTHOR]

Abstract: Instability of continuous-wave (CW) states is investigated in a system of two parallel-coupled fibers, with a pumped (active) nonlinear dispersive core and a lossy (passive) linear one. Modulational instability (MI) conditions are found from linearized equations for small perturbations, the results being drastically different for the normal and anomalous group-velocity dispersion (GVD) in the active core. Simulations of the full system demonstrate that the development of the MI in the former regime leads to establishment of a regular or chaotic array of pulses, if the MI saturates, or a chain of well-separated peaks with continuously growing amplitudes if the instability does not saturate. In the anomalous-GVD regime, a chain of return-to-zero (RZ) peaks, or a single RZ peak emerge, also with growing amplitudes. The latter can be used as a source of RZ pulses for optical telecommunications. [Copyright &y& Elsevier]

Abstract: Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schrödinger equation we will introduce a transformation to displaced phase-amplitude variables with respect to a background of monochromatic waves. The potential energy in the Hamiltonian then depends essentially on the phase. Looking as a special case to phases that are time independent, the oscillator equation for the signal at each position becomes autonomous, with the change of phase with position as only driving force for a spatial evolution towards extreme waves. This is observed to be the governing process of wave amplification in classes of already known solutions of NLS, namely the Akhmediev-, Ma- and Peregrine-solitons. We investigate the case of the soliton on finite background in detail in this Letter as the solution that descibes the complete spatial evolution of modulational instability from background to extreme waves. [Copyright &y& Elsevier]

Abstract: We study the modulational instability of Stokes waves without the traditional assumption as to the movement of a mean flow with the group velocity of the first harmonic. We have shown that the well-known limit , where h is the fluid depth and k is the wave number, for the transition between the states of modulationally stable and unstable fluids in the case of weakly nonlinear waves can be obtained without this assumption. This limit is shown to be shifted to greater kh, as the nonlinearity is strengthened. It is also shown that the disappearance of the modulational instability (restabilization) for small wave numbers of a perturbation, which was predicted on the basis of the Zakharov equations and numerical calculations of the exact equations, does not follow also from a weakly nonlinear theory, provided that the above assumption is not used. [Copyright &y& Elsevier]

Abstract: Modulational instability in a trapped BEC is investigated both analytically and numerically. A new explicit time-dependent criteria for modulational instability of the trapped BEC is obtained. It is shown that a modulational unstable time scale exists. The modulational properties are modified significantly by the external trapping. The theoretical results are verified by the numerical integration of the fully Gross–Pitaevskii equation. [Copyright &y& Elsevier]

The modulational interaction of very short wavelength lower-hybrid waves with slow density modulations associated with inertial Alfven mode is investigated. Nonlinear equations governing this interaction are derived and soliton-like solutions of these equations are discussed in the context of auroral ionosphere. [Copyright &y& Elsevier]