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Acoustic metamaterial concepts, such as metalenses and hyperlenses, have been studied with much interest for super-resolution imaging. However, the physics of wave scattering by sub-wavelength sized defects is still not very well understood. Here, we present studies on acoustic wave interactions with circular defects of sizes varying from over a wavelength to sub-wavelength scale. Near- and far-field scattering patterns of single circular defects are presented, connecting them to analytical frameworks. Scattering field signatures produced by two identical circular defects of different sizes placed side by side are then discussed. The separation distance between the defects is among the parameters varied to understand the effects of geometric features in successful imaging. Experimental results are presented to support the predictions reported in the paper. The insights have important implications for sub-wavelength imaging using acoustic metamaterials. [ABSTRACT FROM AUTHOR]

We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically. [ABSTRACT FROM AUTHOR]

The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium. [ABSTRACT FROM AUTHOR]

In this work, we use two newly powerful and efficient techniques, the unified method and the unified Riccati equation expansion (UREE) method, to derive solitary wave solutions for the (1 + 1)-dimensional longitudinal wave equation (LWE), presenting a systematic approach to reveal the underlying dynamics. By incorporating mathematical analysis and numerical simulations, we investigate the behavior and properties of these solitary wave solutions in various fields of science. The derived solutions are entirely new, and these findings show the essential complexities of the longitudinal wave equation. These obtained solutions shed light on the fundamental mechanisms governing solitary waves in the longitudinal wave equation, contributing to a deeper understanding of nonlinear wave phenomena. We present effective visualizations of the dynamical wave structures using various graphs, such as 3D, 2D, and contour plots in the obtained solutions to improve our comprehensive understanding. Consequently, numerous types of wave profiles, including periodic wave, interaction between periodic wave and kink wave, W-shape wave, kink wave, interaction between breather wave and kink wave, traveling wave, mixed periodic, singular soliton, and some new types of soliton profiles were found. Consequently, this work presents a comprehensive study of solitary wave solutions using the unified method and UREE method for the (1 + 1)-dimensional LWE equation. The outcomes of the current study manifest that the considered methods are significant and systematic in solving nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

In this work, we take into account the (2+1)-Davey Stewartson equation (DSE) and the (2+1)-complex coupled Maccari system (CCMS) and their analytical solutions. Besides, we tackle the role of the problem parameters on the soliton behavior produced by the presented DSE. Exact traveling wave solutions are highly useful in numerical and analytical theories for such equations. While numerical methods are widely used, improving analytical approaches for obtaining analytical solutions is necessary for a deeper understanding of dynamics. This study marks a significant milestone by implementing the efficient analytical approach, enhanced modified extended tanh expansion method, for the first time to the (2+1)-DSE and (2+1)-CCMS equations, thereby making a notable contribution to the existing literature. We have shown that features of the soliton solutions can represent the spread of propagation on the wavefronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three- and two-dimensional arrangements can also be described in graphic representations of their behavior. With the help of the graphical depictions, bright, singular, and periodic singular soliton characters for the (2 + 1) -DSE and singular, dark, bright, and periodic singular soliton characters for the (2 + 1) -CCMS are acquired. The results show that the utilized analytical technique is easily applicable, efficient, reliable, robust, and categorical when it comes to finding analytical solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant influences on the behavior of the solitons of the DSE, and this examination is studied for the first time in this article. [ABSTRACT FROM AUTHOR]

The Gilson–Pickering equation, which describes wave propagation in plasma physics and the structure of crystal lattice theory that is most frequently used. The discussed model is converted into a bilinear form utilizing the Hirota bilinear technique. Sets of case study are kink wave solutions; breather solutions; collision between soliton and periodic waves; soliton and periodic waves. The exp (- θ (α)) -function approach is employed to discover travelling wave solutions including five classes of solutions. In addition, it has been confirmed that the established findings are stable, and it has been helpful to validate the computations. The effect of the free variables on the behavior of obtained solutions to some plotted graphs for the exact cases is also explored depending upon the nature of nonlinearities. The exact solutions are utilized to demonstrate the physical natures of 3D, density, and 2D graphs. [ABSTRACT FROM AUTHOR]

With the developing technology, magneto-optical and ferromagnetic materials are gaining importance and are used especially in magneto-optics, ferromagnetism, fluid mechanics, etc. These processes are modeled via Kadomtsev–Petviashvili-type models. In this work, a generalized (3+1)-dimensional variable-coefficient modified Kadomtsev–Petviashvili (vcmKP) system and special cases are considered that simulates electromagnetic, water, and powder-acoustic/ion-acoustic/dust-ion-acoustic waves. As to the novelty of this paper, the travelling wave, soliton solutions of the considered systems are hold by using Bernoulli method which is the well-known ansatz-based method and the analytical method. As far as we know, the obtained solutions are seen for the first time in this study and are important for the development of the use of magneto-optical and ferromagnetic materials in industry and applied sciences, fiber optic communication fields. [ABSTRACT FROM AUTHOR]

In this research, the solitary wave solutions, the periodic type, and single soliton solutions are attained. The coupled fractional Lakshmanan–Porsezian–Daniel (LPD) equation is depicted the wave pulses' physical properties in birefringent optical fibres containing two vector solitons. Here, the Paul–Painlevé operator is employed to investigate kink soliton solutions. Also, the new modified exponential Jacobi technique is used to find periodic wave and soliton, bright-dark soliton. By utilizing symbolic computation and the applied methods, the mentioned system is successfully investigated. The coupled fractional LPD model is exhibited the travelling waves, as shown by the research in the current paper. Through three-dimensional graph, contour graph, density graph, complex-plot, and two-dimensional design using Maple, the physical features of single soliton and periodic wave solutions are explained all right. The findings the investigated model's broad variety of explicit solutions are demonstrated. As a result, the exact solitary wave solutions to the studied issues, including solitary, single soliton, and periodic wave solution are found. It is shown that the approach is practical and flexible in mathematical physics. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to study the optical soliton solutions and single traveling wave solutions of the generalized stochastic Schrödinger–Hirota equation in magneto-optic waveguides. With the help of the complete discriminant system technique and symbolic computation, a range of new single traveling wave solutions and optcial solitons are derived, which include Jacobian elliptic function solutions, dark solitons, trigonometric function solutions, singular solitons, rational function solutions, hyperbolic function solutions, periodic wave solutions and solitary wave solutions. Lastly, in order to understand mechanisms of complex physical phenomena and dynamical processes for the generalized stochastic Schrödinger–Hirota equation in magneto-optic waveguides, two-dimensional and three-dimensional diagrams are also drawn. [ABSTRACT FROM AUTHOR]

This paper investigates (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) system equations using the improved Sadar subequation method. It uncovers analytical solutions, including dark solitons, bright solitons, and periodic waves. The dynamic behavior of these solutions is illustrated through 2D and 3D plots by adjusting parameters. The results highlight the effectiveness and simplicity of the proposed methods, providing a versatile approach to obtaining various traveling wave solutions. These findings are expected to advance the shallow water theory of ideal fluids. [ABSTRACT FROM AUTHOR]

The purpose of the presented work is to obtain the exact solutions of the Paraxial wave equation using two different methods, the modified auxiliary equation method and G ′ G , 1 G -expansion method. Results obtained by these methods are unique. The paraxial wave equation is a partial differential equation that describes the propagation of optical waves in the paraxial approximation. This equation is derived from Maxwell's equations, which describe the behavior of electromagnetic waves. The paraxial wave equation is a fundamental tool in optics for analyzing the propagation of optical waves in the paraxial approximation. The application of integrating techniques allows researchers and engineers to obtain solutions and predict the behavior of optical systems in a wide range of applications. As a result of modified auxiliary equation method and G ′ G , 1 G -expansion method, new soliton solutions of the given model are extracted. These solutions include hyperbolic solutions and periodic solutions. The necessary constraint conditions for the existence of solutions are also provided. Moreover, for appropriate parametric values, acquired findings are displayed via contour, 2D and 3D graphics that show the physical relevance and dynamical behaviors of the proposed equation. It is noticed that proposed methods are well organized and efficient in obtaining accurate solutions for many nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The Hamiltonian amplitude equation that describes the transmissions of wire optical technology along wave propagation in the physics linked disciplines can be solved by utilizing the unique analytical and semi-analytical approaches namely the polynomial expansion method and the Adomian decomposition technique. Various types of soliton solutions are attained that express different behaviours including singular and v-shaped soliton solutions behaviour. The developed solutions are highly important in dealings the wave behaviour in mathematical physics related fields and in the transmission of optical fibers. The approaches applied in this paper are not utilized in given model so we apply these strategies to attain the soliton solutions. Hence we conclude the the results attained are unique, robust and newly made that proves novelty of the work. Furthermore, we study the stability plus the modulation instability of the given model. The 3D, contours, and 2D graphics are visualised to demonstrate the dynamical structures of the established results more efficiently. [ABSTRACT FROM AUTHOR]

In this article, two most prominent models namely the Camassa–Holm nonlinear Schrödinger equation and the (3 + 1) -dimensional Boussinesq equation have been investigated for extracting new and novel solitary wave solutions. The Camassa–Holm nonlinear Schrödinger (CHNLS) equation is a mathematical model that combines the features of two important equations in physics: the Camassa–Holm equation and the nonlinear Schrödinger equation. The Camassa–Holm equation describes the propagation of shallow water waves over a flat bottom, and has soliton solutions with sharp peaks called peakons. The nonlinear Schrödinger equation describes the evolution of wave packets in nonlinear and dispersive media, and has soliton solutions with smooth profiles. The CHNLS equation has been addressed analytically to determine the exact solutions by implementing extended G ′ / G 2 -expansion approach. The Boussinesq equation is a mathematical model that is capable of simulating weakly nonlinear and long-wave approximations is also solved analytically by applying extended G ′ / G 2 -expansion approach. This model finds its applications in various fields such as coastal engineering, and numerical models for water wave simulation in harbors and shallow seas. The two considered equations have significant applications in mathematical physics and their exact wave solutions are essential to understand their dynamical behavior. Dark solitons, bright solitons, and periodic waves are observed from the obtained results. It is reasonable to say that our approach provides an impressive mathematical mechanism for producing traveling wave solutions for numerous mathematical and physical models. Also our proposed method improves the accuracy of the solution. The technique employed here is basic and concise. Graphs are presented to depict the behavior of some of the retrieved dynamical wave structures. All computations are done using the mathematical software Maple. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of a class of reaction-advection-diffusion equations of the form u t − Δ u + β (y) u x = f (t , u) in cylinders, where f is a tristable or multistable nonlinearity satisfying f (⋅ , 0) = f (⋅ , 1) = 0. We establish the alternative of wave solutions, that is, either there is a unique, asymptotically stable periodic traveling wave connecting 0 to 1 directly, or there is a unique propagating terrace connecting 0 to 1. Under the assumption that all wave speeds in propagating terrace are not equal to each other, we further obtain that the propagating terrace is asymptotically stable if it exists. Moreover, the sufficient and necessary conditions for the existence of periodic traveling waves connecting 0 to 1 are given respectively. Our arguments are based on the parabolic maximum principle, sliding method and the super- and sub-solution method. [ABSTRACT FROM AUTHOR]

The (2 + 1) -dimensional coupled nonlinear Schrödinger equation has versatile applications for modeling nonlinear waves in different areas such as optics, atmospheric science, fluid dynamics, and plasma physics. This study focuses on the propagation of optical solitons and their interaction within various mediums such as multi-mode fiber and fiber arrays. The Sardar-subequation method is applied to achieve the bright, dark, combined bright–dark, periodic, combined dark-singular and singular optical solitons solutions. The 3D, contour and 2D profiles for some of the assimilation solutions are also plotted to show the physical behavior of the solutions. The obtained results demonstrate the effectiveness of the adopted methodology in obtaining traveling wave solutions and have many applications in applied mathematics and engineering. The novelty of our work lies in the successful application of Sardar-subequation method in obtaining diverse soliton solutions and exploring their physical behavior. This study goes beyond previous efforts in the literature by presenting a comprehensive analysis of soliton dynamics. This ability to describe and predict the behavior of optical solitons in diverse mediums opens up new opportunities for investigating the existing systems. [ABSTRACT FROM AUTHOR]

This paper investigates different kinds of exact solutions of variable-coefficients Chiral Schrödinger equation (VCCNLSE). In this equation, the fractional quantum Hall effect edge states are described. By the unified method, we successfully get the soliton, solitary and elliptic wave solutions. Through the (G ′ / G) -expansion and the exponential expansion methods, we acquire different traveling wave solutions. Using the extended F -expansion method, we attain the Jacobi elliptic function solutions. So as to get more physical information about the exact solutions of VCCNLSE, 3D, 2D , density and contour maps are described. [ABSTRACT FROM AUTHOR]

A new method is proposed to predict the topological properties of 1D periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry–Zak phase. Since the characterization of the topological properties is done in the complex plane, it can easily be extended to the case of non‐Hermitian systems. The sequence of poles and zeros allows to predict topological phase transitions. [ABSTRACT FROM AUTHOR]

This article mainly explores the Biswas–Milovic equation containing Kudryashov's refractive index law and nonlinear perturbation terms. We take the complete discrimination system for polynomial method and the trial equation method to implement qualitative and quantitative studies for the equation. We verify that the Hamiltonian of the dynamic system is conserved and apply the complete discrimination system of polynomial method to give the associated global phase diagrams, which are qualitatively analyzed to illustrate the presence of periodic solutions and solitons. In addition, we gain a classification of all single traveling wave solutions, provide optical wave patterns with specific parameters and validate the above findings. [ABSTRACT FROM AUTHOR]

In this study, Γ-shaped rectangular resonators, which are created in a metal insulator metal (MIM) structure, have been studied analytically and numerically. The metal is silver and rectangular resonators are filled by Si and the peak of transparency profile is tuned in the communication band with proper geometrical parameters. By employing 2-D finite difference time domain method (FDTD), simulations show a plasmonic induced transparency (PIT) window in the transmission diagram. The PIT is created by instructive and destructive interference between bright and dark resonator modes. The presented structure demonstrates tunable transparency window by variation of symmetry parameter, s. The maximum group velocity is obtained 0.1 ps in communication band corresponded to 30 μm traveling of light in the vacuum which is comparable to previous articles. The proposed structure may have potential applications in optical memory and delay blocks in designing integrated optical circuits. [ABSTRACT FROM AUTHOR]

In this study, we explore a captivating (3+1)-dimensional negative-order Korteweg–de Vries Calogero–Bogoyavlenskii–Schiff equation, which combines elements of the Korteweg–de Vries equation and the Calogero–Bogoyavlenskii–Schiff equation. Our research investigates how this model characterises long-wave interactions and its relevance in mathematics, physics, and engineering. We employ unified and singular manifold methods to obtain precise travelling wave solutions expressed in various functional forms. By using Maple and Mathematica software to extract valid solutions, including kink-like soliton, singular periodic wave solution, anti-kink solutions, and singular solitons. These methodologies have shown impressive efficiency in solving complex nonlinear equations, offering precise solutions, and streamlining mathematical processes through transformations. This leads to quicker and more accurate outcomes in diverse scientific and engineering applications. Our findings underscore the model's superiority over existing methods and its importance in comprehending applied mathematical processes, as demonstrated through 3-D and 2-D graphical representations. [ABSTRACT FROM AUTHOR]

In our investigation, we've utilized an advanced computational technique, the modified exp - ϕ (ζ) -expansion method, to derive precise solitary wave solutions within the (2+1)–dimensional Ablowitz–Kaup–Newell–Segur (AKNS ) equation. These solutions, categorized by peak amplitudes, wave speeds, and widths, underscore the efficacy and reliability of our approach compared to conventional numerical methods. The significance of our study extends to practical applications of the (2+1)–dimensional AKNS equation in modeling various physical phenomena, from nonlinear optics to water waves and plasma physics. Our research, by precisely determining solitary wave solutions, not only deepens our comprehension of these phenomena but also establishes a robust basis for practical applications. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

The study of water waves is significant for researchers working in many branches of science. The behaviour of waves can be studied by observation or experimental means, but theoretically, mathematical modeling provides solutions to many problems in physics and engineering. Progress in this field is inevitable, with those who work in mathematics, physics, and engineering putting forth interdisciplinary studies. Jacobi elliptic functions are valuable mathematical tools that can be applied to various aspects of mathematics, physics, and ocean engineering. In this study, traveling wave solutions of the general Drinfel'd-Sokolov-Wilson (DSW) system, introduced as a model of water waves, were obtained by using Jacobi elliptic functions and the wave dynamics were examined. The extended Jacobi elliptic function expansion method is an effective method for generating periodic solutions. It has been observed that the periodic solutions obtained by using Jacobi elliptic function expansions containing different Jacobi elliptic functions may be different and some new periodic solutions can be obtained. 3D simulations were made using MapleTM to see the behaviour of the solutions obtained for different appropriate values of the parameters. 2D simulations are presented for easy observation of wave motion. In addition, we transformed the one of the exact solutions found by the extended Jacobi elliptic function expansion method into the new solution under the symmetry transformation. [ABSTRACT FROM AUTHOR]

The present study focuses on the acquisition of traveling wave solutions associated with the conformable time-fractional Zoomeron equation through the utilization of the modified exponential function method (MEFM). The solution functions derived from mathematical computations encompass hyperbolic, trigonometric, and rational functions. Various graphical representations, such as 2D, 3D, contour graphs, and density graphs, are utilized to visually depict the distinct features of the solution functions derived from the determination of suitable parameters. [ABSTRACT FROM AUTHOR]

Gravity currents are of high interest both for their relevance in natural scenarios and because varying horizontal buoyancy presents a canonical problem in fluid mechanics [Huppert, "Gravity currents: A personal perspective," J. Fluid Mech. 554, 299–322 (2006)]. In this paper, attention is directed to gravity currents with a full-depth lock release propagating into a linearly stratified ambient fluid. For the case of an unstratified ambient, similarity solutions are known to capture the evolving height profile of the gravity current. We will compare this solution class with numerical data from high fidelity simulations. The presence of ambient stratification (quantified by the stratification intensity, S) introduces internal gravity waves that interact with the propagating current head, which will inhibit Kelvin–Helmholtz billows, decelerate current propagation, and smooth the shape of the current head. We perform direct numerical simulations of planar two- and three-dimensional gravity currents released into stratified ambient fluid of varying S and analyze the gravity current kinematics. Our analysis complements existing findings from performed laboratory and numerical experiments [Dai et al., "Gravity currents propagating at the base of a linearly stratified ambient," Phys. Fluids 33, 066601 (2021)] that show a stratified ambient modifies the current front velocity. Previous literature employed has inconsistent Reynolds numbers and boundary conditions, complicating interpretations. In the present numerical campaign, a closer analysis clarifies influence of the top boundary condition choice on formation and structure of the internal gravity waves. While acknowledging there is no available choice for a high-accuracy simplified numerical representation of a free-surface, a family of profiles for internal wave formation emerges varying with buoyancy Reynolds number and top boundary condition selection. The subsequent results appraise similarity solutions for the distribution of the heavy fluid in the gravity current. Our results show that for unstratified and low stratification ambient fluid, height profiles permit a similarity solution but higher values of S are less amenable; these profiles suggest a continuing time dependency on the traveling internal wave. [ABSTRACT FROM AUTHOR]

The modified unstable nonlinear Schrödinger equation governs specific instabilities observed in modulated wave-trains and also describes the time evolution of disturbances in marginally stable or unstable media. In this article, we explore the modified unstable dynamical model analytically using three symbolic computational techniques: the positive quadratic function approach, the three-wave approach, and the double exponential approach. As a result of our analysis, we have derived novel exact solutions, including rational solitons, multi-wave solutions, and other types of wave solutions for this dynamical model. These solutions are obtained through symbolic computation and the ansatz function method, incorporating both traveling wave and logarithmic transformations. The derived wave solutions hold practical significance, contributing significantly to understanding the physical phenomena of this complex model. We also computed conservative quantities such as power, momentum, and energy associated with solitons. To evaluate the stability of this modified unstable equation, we conducted a comprehensive modulational instability analysis, confirming the stability and exactness of all soliton solutions. By selecting appropriate parameter values, we generated 3D visual representations in various forms, including breather-type waves, lump waves, multi-peak solitons, etc. Furthermore, our observations revealed intriguing phenomena arising from the interactions among these multi-waves, with applications spanning a wide range of scientific and engineering disciplines. [ABSTRACT FROM AUTHOR]

The (2+1)-dimensional extended Calogero–Bogoyavlenskii–Schiff equation appears in the mathematical description of physical phenomena in plasma physics, fluid dynamics and nonlinear optics. In this article, extended trial and modified auxiliary equation methods are utilized to observe the dynamical structures exhibiting the solitary wave behavior of the considered model. The traveling wave hypothesis is employed to extract explicit closed-form solution expressions. The presented methods show reliability and robust computational capabilities to investigate solitary waves. In order to investigate the physical behavior of these solutions, 3D, 2D and density plots are drawn for different values of parameters. The graphical observations depict kink soliton, dark–bright singular soliton and periodic wave solutions. The comparison of the outcomes of the proposed results with those obtained using prior techniques is made to confirm the usefulness of the proposed techniques. The presented study will be helpful to explain the wave propagation in many problems of plasma physics and fluid dynamics. Moreover, the reported solutions may help to understand optical wave transmission and aid in the development of optical devices. The results given in this study will contribute in the understanding of the behavior of waves in the higher-dimensional governing models. [ABSTRACT FROM AUTHOR]

In this investigation, we utilize two recent analytical schemes to unveil novel solitary wave solutions for the (1 + 1) -dimensional Mikhailov–Novikov–Wang integrable equation. The said equation serves as a mathematical model that captures specific physical phenomena, albeit lacking a direct physical interpretation. Nevertheless, it finds relevance in various systems within the realm of nonlinear waves in physics. Through the application of the aforementioned analytical schemes, we derive fresh solutions and evaluate their accuracy by employing the variational iteration method. The congruence observed between the analytical and numerical solutions of the investigated model serves as validation for the constructed solutions. Furthermore, we delve into exploring the implications of obtaining precise and ground breaking solitary wave solutions on the practical applications associated with the studied model. [ABSTRACT FROM AUTHOR]

The area of fractional partial differential equations has recently become prominent for its ability to accurately simulate complex physical events. The search for traveling wave solutions for fractional partial differential equations is a difficult task, which has led to the creation of numerous mathematical approaches to tackle this problem. The primary objective of this research work is to provide optical soliton solutions for the Frictional Kundu–Eckhaus equation (FKEe) by utilizing generalized coefficients. This strategy utilizes the Riccati–Bernoulli sub-ODE technique to effectively discover the most favorable traveling wave solutions for fractional partial differential equations. As a result, it facilitates the extraction of optical solitons and intricate wave solutions. The Backlund transformation is used to methodically construct a sequence of solutions for the specified equations. The study additionally showcases 3D and Density graphics that visually depict chosen solutions for certain parameter selections, hence improving the understanding of the outcomes. [ABSTRACT FROM AUTHOR]

Orbit angular momentum (OAM) has been considered a new dimension for improving channel capacity in recent years. In this paper, a millimeter-wave broadband multi-mode waveguide traveling-wave antenna with OAM is proposed by innovatively utilizing the transmitted electromagnetic waves (EMWs) characteristic of substrate-integrated gap waveguides (SIGWs) to introduce phase delay, resulting in coupling to the radiate units with a phase jump. Nine "L"-shaped slot radiate elements are cut in a circular order at a certain angle on the SIGW to generate spin angular momentum (SAM) and OAM. To generate more OAM modes and match the antenna, four "Π"-shaped slot radiate units with a 90° relationship to each other are designed in this circular array. The simulation results show that the antenna operates at 28 GHz, with a −10 dB fractional bandwidth (FBW) = 35.7%, ranging from 25.50 to 35.85 GHz and a VSWR ≤ 1.5 dB from 28.60 to 32.0 GHz and 28.60 to 32.0 GHz. The antenna radiates a linear polarization (LP) mode with a gain of 9.3 dBi at 34.0~37.2 GHz, a l = 2 SAM–OAM (i.e., circular polarization OAM (CP–OAM)) mode with 8.04 dBi at 25.90~28.08 GHz, a l = 1 and l = 2 hybrid OAM mode with 5.7 dBi at 28.08~29.67 GHz, a SAM (i.e., left/right hand circular polarization (L/RHCP) mode with 4.6 dBi at 29.67~30.41 GHz, and a LP mode at 30.41~35.85 GHz. In addition, the waveguide transmits energy with a bandwidth ranging from 26.10 to 38.46 GHz. Within the in-band, only a quasi-TEM mode is transmitted with an energy transmission loss | S 21 | ≤ 2 dB. [ABSTRACT FROM AUTHOR]

In this paper, we consider a reaction-diffusion cholera model with hyperinfectious vibrios and spatio-temporal delay. In the model, it is assumed that cholera has a fixed latent period and the latent individuals can diffuse, and a non-local term is incorporated to describe the mobility of individuals during the latent period. It is shown that the existence and nonexistence of traveling wave solutions are fully determined by the basic reproduction number R 0 and the critical wave speed c*. Firstly, when R 0 > 1 and the wave speed c > c*, the existence of strong traveling waves is obtained by using Schauder's fixed point theorem and Lyapunov functional approach. By employing a limiting argument, the existence of strong traveling waves is established when R 0 > 1 and c = c*. Next, when R 0 ≤ 1 , the nonexistence of traveling wave solutions is established by contradiction. Besides, when R 0 > 1 and c < c*, the nonexistence of traveling wave solutions is obtained by means of two-sided Laplace transform. This indicates that c* is indeed the minimal wave speed. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This article reveals the different types of optical solitons of non-linear coupled Riemann wave equation and Wazwaz Kaur Boussinesq equation. We adopted a direct integration technique namely, modified G ′ G 2 -expansion. Different sorts of soliton's existence criteria are also presented here. The proposed technique provides the new travelling wave solutions with the aid of different types of derivatives such as beta derivative, M-Truncated derivative and Conformable derivative and also offers special kinds of solutions including rational, trigonometric and hyperbolic solutions. In this work, we compared and analysed solitary wave solutions obtained by using different types of fractional derivatives. The outcomes of the study are highly significant for modern communication network technology, optical fiber, ion-acoustic, magneto-sound waves in plasma, and stationary media, particularly in the propagation of tidal and tsunami waves. [ABSTRACT FROM AUTHOR]

This paper explores the dynamic behavior of the (2 + 1) -dimensional Boussinesq equation, which is a nonlinear water wave equation used to model wave packets in dispersive media with weak nonlinearity. Specifically, we investigate the equation's traveling wave solutions using the Riccati equation mapping method. Our results include solitary and soliton solutions, each with their own set of parameter values. To provide a comprehensive understanding of these solutions, we present them in general form and visualize their significance using various graphs, such as 3D, 2D, and contour plots. The computational effort and resulting outcomes highlight the efficacy of our approach, which has the potential to be applied to other nonlinear physical problems in fields such as mathematical physics, engineering, and nonlinear science. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical approach for studying the changes in pressure and temperature variables in flames. This conception extends beyond the traditional second-order Laplacian diffusion model by considering the p-Laplacian operator and a bi-stable reaction term, thereby providing a more generalized framework for flame diffusion analysis. Given the structure of our equations, we provide the boundedness and uniqueness of the solutions in a weak sense from both analytical and numerical approaches. We further reformulate the governing equations in the context of traveling wave solutions, applying singular geometric perturbation theory to derive the analytical expressions of these profiles. This theoretical development is complemented by numerical assessments, which not only validate our theoretical predictions, but also optimize the traveling wave speed to minimize the error between numerical and analytical solutions. Additionally, we explore self-similar structured solutions. The paper then concludes with a perspective on future research, with emphasis being placed on the need for experimental validation in laboratory settings. Such empirical studies could test the robustness of our model and allow for refinement based on actual measurements, thereby broadening the applicability and accuracy of our findings in practical scenarios. [ABSTRACT FROM AUTHOR]

The motion of a heavy mass on a bridge span causes vibrations whose magnitude and frequency content depend on the mechanical properties of the structural system, including the magnitude of that mass and its speed of traverse. In order to limit vibrations that could potentially cause damage, a simple passive device configuration, namely the tuned mass damper (TMD), is introduced and its effect on the beam vibrations analyzed. Specifically, a TMD in the form of a single-degree-of-freedom (SDOF) unit comprising a mass and a spring is placed on the span to act as a secondary system for absorbing vibrations from the primary system, i.e., the bridge itself. A Lagrangian energy balance formulation is used to derive the governing equations of motion, followed by an analytical solution using the Laplace transform to investigate the transmission of vibratory energy between primary and secondary systems. Results are given in terms of time histories, Fourier spectra and spectrograms, where the influence of the TMD in reducing vibratory energy is demonstrated. The TMD is placed in the region where the beam's transverse motion is at a maximum, while its mechanical properties are sub-optimal, in the sense that there is no separate damper present and minimal damping is provided by the spring element itself. In parallel with the analysis, a series of experiments involving a simply supported model steel bridge span traversed by a heavy mass are conducted to first gauge the analytical solution and then to confirm the validity of the proposed passive scheme. [ABSTRACT FROM AUTHOR]

To tackle the challenge of localization failure due to traveling wave dispersion during a mid-line fault in a long high-voltage cable, this study conducts an in-depth analysis of the refraction characteristics of the cumulative three-phase sheath currents at cross commutation points and direct grounding points, facilitated by detailed theoretical derivation. We introduce the novel concept of a 'first traveling wave attenuation index,' which quantifies the peak of the initial faulted traveling wave. We strategically place distributed traveling wave detection devices solely in the first direct grounding box of each cross-interconnected main section, effectively segmenting the line into five distinct zones. These zones are identified based on the unique transient polarities exhibited by the first traveling wave of fault current at each impedance mismatch point along the cable. To overcome the issue of weak traveling wave signals collected at the first end measurement point, we propose an innovative peak detection method for the first wave. This method harnesses the power of empirical wavelet transform (EWT) and multi-resolution singular value decomposition (MRSVD), providing a significant boost in ranging accuracy compared to traditional wavelet methods. Simulation results validate the efficacy of our proposed fault location method, which accurately pinpoints the fault section by contrasting the polarity of the first wave peak of the sheath current detected at each measurement point. Notably, our method ensures safety and convenience as the equipment does not require direct contact with high voltage. [ABSTRACT FROM AUTHOR]

Studies into scatterings of photonic structures have been so far overwhelmingly focused on their dependencies on the spatial and spectral morphologies of the incident waves. In contrast, evolutions of scattering properties through another parameter space of incident directions (momentum space) has not attracted sufficient attention, with the underlying general governing rules still unrevealed. Here, from the perspective of quasi‐normal modes (QNMs), the momentum‐space scattering extremizations with respect to varying incident directions of plane waves are investigated. It is revealed that for effective single‐QNM excitations, scatterings are maximized exactly along those directions where the QNM radiation reaches its maximum, with matched incident and radiation polarizations. For an arbitrary direction, when the incident polarization is tuned to be orthogonal to that of the mode radiation, the QNM cannot be excited and thus the scatterer becomes invisible with null scatterings. The principles revealed are protected by fundamental laws of reciprocity and energy conservation (optical theorem), which can be further expanded and applied for other branches of wave physics. [ABSTRACT FROM AUTHOR]

This work deals with high-k modes of the ion cyclotron emission (ICE)—the modes with frequencies close to ion cyclotron harmonics and wave numbers well exceeding those of fast magnetoacoustic modes (FMM). These modes exist due to finite Larmor radius of the ions. They are responsible for the ICE recently observed in the DIII-D tokamak [N. A. Crocker et al., Nucl. Fusion 62, 026023 (2022)]. The work is aimed at knowing the radial structure of high-k eigenmodes. Its analysis is relied on a comprehensive study carried out by employing a general dispersion equation for traveling waves, which allowed to group modes and determine conditions of their existence. Differential equations for various eigenmodes (standing waves) were obtained and analyzed. In particular, electrostatic modes and electromagnetic modes with various ratios of the longitudinal phase velocity to the electron thermal velocity were considered. A numerical code solving these equations was developed. It is found that high-k modes with sufficiently large poloidal mode numbers are located at the plasma periphery, and their amplitudes in the plasma core are very small. It is concluded that high-k modes are not an exceptional case, although presumably FMMs can explain most ICE experiments. They exist in plasmas with various magnitudes of β, representing different wave branches associated with finite Larmor radius of the ions. The mentioned experiment on DIII-D is discussed. [ABSTRACT FROM AUTHOR]

Thermoacoustic refrigerators exploit the thermodynamic interaction between oscillating gas particles and a porous solid to generate a temperature gradient that provides a cooling effect. In this work, we present a resonator with dual enclosed driver end-caps and show that the temperature gradient across a ceramic thermoacoustic element placed in the cavity could be controlled by modifying the phase difference of the drivers, thus enabling precise control of the refrigeration capability via the temperature difference. Through deltaec simulation results, the response of the temperature gradient to various dynamic boundary conditions that alter the time-phasing and wave dynamics in the resonator are demonstrated. An experimental apparatus is constructed with two moving-coil speakers and a ceramic stack, which is shown to exhibit a temperature gradient along its length, based on the traveling-wave-like nature of the acoustic wave excited by the speakers. By adjusting the relative phase lag between the two speakers, the temperature gradient across the stack is made to increase, decrease, or flip sign. Finally, a desired temperature difference that changes in time is achieved. The results presented in this work represent a key conceptual advancement of thermoacoustic-based temperature control devices that can better serve in extreme environments and precision applications. [ABSTRACT FROM AUTHOR]

This article proposes using the theremin, an electronic musical instrument invented in 1920, as a tool to teach introductory physics and electronics concepts. The theremin consists of two metallic antennae that control the volume and pitch of the sound emitted. The article suggests that the theremin can be used to teach concepts such as wave physics, electricity, and electronics. Different low-cost theremin prototypes based on Arduino are also described, which can be built by students themselves. The use of the theremin as a learning tool is particularly relevant in the post-2020 era due to its hands-free operation, which aligns with the need for sanitary guarantees in learning activities. [Extracted from the article]

We develop a novel approach for multi‐frequency, elliptical‐anisotropic eikonal tomography based on physics‐informed neural networks (pinnEAET). This approach simultaneously estimates the medium properties controlling anisotropic Rayleigh waves and reconstructs the traveltimes. The physics constraints built into pinnEAET's neural network enable high‐resolution results with limited inputs by inferring physically plausible models between data points. Even with a single source, pinnEAET can achieve stable convergence on key features where traditional methods lack resolution. We apply pinnEAET to ambient noise data from a dense seismic array (ChinArray‐Himalaya II) in the northeastern Tibetan Plateau with only 20 quasi‐randomly distributed stations as sources. Anisotropic phase velocity maps for Rayleigh waves in the period range from 10–40 s are obtained by training on observed traveltimes. Despite using only about 3% of the total stations as sources, our results show low uncertainties, good resolution and are consistent with results from conventional tomography. Plain Language Summary: Anisotropy refers to the directional dependence of seismic wave velocities, which can arise from a variety of factors such as crystal alignment, stress fields, or fluid‐filled cracks. Elliptical‐anisotropic eikonal tomography is a variant of eikonal tomography that can be used to estimate medium properties and reconstructed traveltimes from ambient noise data. In this study, we propose a new algorithm to implement multi‐frequency, elliptical‐anisotropic eikonal tomography based on physics‐informed neural networks (pinnEAET), which combine data‐driven models with theory‐based models that include physics constraints on the system. We apply this architecture to data from a dense seismic array deployed on the northeastern Tibetan Plateau. Our results can achieve at least the same resolution as traditional methods while requiring less traveltime data. This strategy can provide new insights into the seismic imaging in case of limited or noisy data. Key Points: We present a physics‐informed deep learning eikonal tomography method for anisotropic velocity modelingThe algorithm incorporates wave physics to simultaneously process multi‐frequency data, ensuring reliable tomographic modelsWe successfully recover the anisotropic velocity structure of the northeastern Tibet using less data than in traditional models [ABSTRACT FROM AUTHOR]

In this paper, We have developed a variety of new approximate solutions for the nonlinear fractional generalized Pochhammer-Chree equation (FGPCEs) using the fractional homotopy perturbation transform method via the Caputo-Fabrizio fractional derivative(CFFD) of order α where α ∈ (1 , 2 ]. via Laplace transform technique.we investigate all concerned wave models that have been used in the examination for the propagation of harmonic waves in a cylindrical rod and several problems in fluid mechanics and wave theory in physics. Banach's fixed point hypothesis is tested for governing the fractional-order model in order to establish the existence and uniqueness of the achieved solution. We considered the model in terms of arbitrary order with three cases and introduced corresponding numerical simulations to demonstrate and validate the effectiveness of the proposed algorithm. By assigning appropriate values to free parameters, dynamical wave structures of some approximate solutions are graphically demonstrated using 2D and 3D Fig. This method can also be used to approximate the solutions of other well-known equations in engineering physics, quantum field, and other applied sciences. Furthermore, various simulations are used to demonstrate the physical behaviors of the acquired solution with respect to fractional integer order. [ABSTRACT FROM AUTHOR]

Asymmetric manipulation of acoustic waves has gained significant attention due to its rich physical properties and potential application prospects. In this study, we design and demonstrate a planar acoustic metasurface (AM) that enables asymmetric conversion for vortex fields with arbitrary orbital angular momentum (OAM) to different plane waves by placing the same vortex source at different focusing points of above and below. This asymmetric effect is caused by the spatial asymmetry of vortex wave, and AM achieves the conversion of two types of waves through directional compensation of phases. Numerical demonstrations and acoustic experiments further validate this asymmetric phenomenon, and the deflection angle of converted plane waves is qualitatively and quantitatively confirmed by a more general formula. Our work enriches the research meta-system of acoustic wave physics and holds potential applications in underwater acoustic communication and OAM-based devices. [ABSTRACT FROM AUTHOR]