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The nonlinear Kadoma equation with M-truncated derivatives (NLKE-MTD) is taken into consideration here. By using generalized Riccati equation method (GRE method) and Jacobi elliptic function method, new hyperbolic, rational, trigonometric and elliptic solutions are discovered. Because the NLKE is widely employed in optics, fluid dynamics and plasma physics, the resulting solutions may be used to analyze a wide variety of important physical phenomena. The dynamic behaviors of the different derived solutions are interpreted using 3D and 2D graphs to explain the effects of M-truncated derivatives. We may conclude that the surface moves to the right as the order of M-truncated derivatives increases. [ABSTRACT FROM AUTHOR]

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections. [ABSTRACT FROM AUTHOR]

This research explores the dual-mode manifestation within the nonlinear Schrödinger equation, elucidating the amplification or absorption of paired waves. This study delves into the simultaneous generation of two distinct waves associated with the dual-mode phenomenon with three crucial parameters: phase velocity, nonlinearity and dispersive factor. The resulting wave phenomena from these solutions have implications across various fields, including fluid dynamics, water wave mechanics, ocean engineering and scientific inquiry. The study employs the modified Sardar sub-equation method to obtain the optical soliton solutions, encompassing various types such as dark, bright, singular, combo dark–singular, periodic singular and dark–bright solitons. The obtained results highlight the reliability and simplicity of the modified Sardar sub-equation method. Additionally, the paper delves into the parametric conditions crucial for shaping and sustaining these solitons. The research explores the interaction of dual waves and the variation in wave speed. Furthermore, dynamic phenomena are illustrated, and the physical implications of the solutions are interpreted using 3D and 2D plots with different parameter values. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is the investigation of the truncated M fractional Kuralay equation, which finds applicability in various domains such as engineering, nonlinear optics, ferromagnetic materials, signal processing, and optical fibers. As a result of its capacity to elucidate a vast array of complex physical phenomena and unveil more dynamic structures of localized wave solutions, the Kuralay equation has received considerable interest in the scientific community. To extract the solutions, the recently developed integration method, referred to as the modified generalized Riccati equation mapping (mGREM) approach, is utilized as the solving tool. Multiple types of optical solitons, including mixed, dark, singular, bright-dark, bright, complex, and combined solitons, are extracted. Furthermore, solutions that are periodic, hyperbolic, and exponential are produced. To acquire a valuable understanding of the solution dynamics, the research employs numerical simulations to examine and investigate the exact soliton solutions. Graphs in both two and three dimensions are presented. The graphical representations offer significant insights into the patterns of voltage propagation within the system. The aforementioned results make a valuable addition to the current body of knowledge and lay the groundwork for future inquiries in the domain of nonlinear sciences. The efficacy of the modified GREM method in generating a wide range of traveling wave solutions for the coupled Kuralay equation is illustrated in this study. [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 is mainly concerning the study of truncated M-fractional Kuralay equations that have applications in numerous fields, including nonlinear optics, ferromagnetic materials, signal processing, engineering fields and optical fibers. Due to its ability to clarify a wide range of sophisticated physical phenomena and reveal more dynamic structures of localized wave solutions, the Kuralay equation has captured a lot of attention in the research field. The newly designed integration methods, known as the modified Sardar subequation method and enhanced modified extended tanh expansion method are used as solving tools to validate the solutions. The goal of this study is to extract several kinds of optical solitons, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. Due to the many potential applications for superfast signal routing techniques and shorter light pulses in communications, the optical propagation of soliton in optical fibers is now a topic of significant interest. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. In addition, exponential, periodic, hyperbolic solutions are generated. The applied approaches are efficient in explaining fractional nonlinear partial differential equations by providing pre-existing solutions and also producing new solutions by combining results from multiple processes. Additionally, we plot the contour, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The results of this study show the effectiveness of the approaches adopted and help enhance comprehension of the nonlinear dynamical behavior of specific systems. We expect that a substantial amount of engineering model specialists will greatly benefit from our work. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems. [ABSTRACT FROM AUTHOR]

This paper deals with the soliton solutions for beam movement within a multimode optical fiber featuring a parabolic index shape. It is considered that a Two-Dimensional Nonlinear Schrödinger Equation (2D-NLSE) with an instantaneous Kerr nonlinearity of the kind can represent the beam dynamics. Nonlinear Multimode Optical Fibers (MMFs) of this kind are gaining popularity because they provide novel approaches to control the spectral, temporal, and spatial characteristics of ultrashort light pulses. We gain the optical soliton solutions for the nonlinear evolution beam dynamics using the Jacobi Elliptic Function Expansion (JEFE) method. The exact analytical solution of Nonlinear Partial Differential Equations (NLPDEs) can be achieved with wide application using the effective JEFE approach. These solutions are obtained in the form of dark, bright, combined dark–bright, complex combo, periodic, and plane wave solutions. Additional solutions for Jacobi elliptic functions, encompassing both single and dual function solutions, have been acquired. This approach is based on Jacobi elliptic functions, which will provide us the exact soliton solutions to nonlinear problems. Additionally, we will analyze the Modulation Instability (MI) for the underlying model. Moreover, we show the physical behavior of the beam propagation in a multimode optical fiber the three-dimensional, two-dimensional, and their corresponding contour plots are dispatched using the different values of parameters. [ABSTRACT FROM AUTHOR]

In this paper, the nonparaxial nonlinear Schrödinger (NNLS) equation by considering its integrability which enables the propagation of ultra-broad nonparaxial beams in a planar optical waveguide is studied. The plenty numbers of solitary wave solutions by using Hirota's bilinear scheme are found, in addition, the bilinear transformation and also the related theorem for getting to the bilinear form of nonlinear system are considered. Two new simple approaches are implemented to recover periodic wave, bright soliton, singular, and singular soliton for this model. Because of the significance of the NNLS in modeling the propagation of solitons through an optical fiber, the recovered solitons are vital for describing and understanding a variety of fundamental physical processes. The effect of the free parameters on the behavior of acquired figures to a few obtained solutions by providing the feasibility and reliability of the used procedure was also discussed. For more physical illustration and knowledge of the physical characteristics of this equation, some important solutions are discussed graphically in the form of 2D and 3D plots by selecting suitable parameters. [ABSTRACT FROM AUTHOR]

In this paper, the thermophoretic motion equation based on Korteweg–de Vries is utilized to analyze new complexiton and soliton-like solutions. The homogenous balance approach is employed to generate auto-Bäcklund transformation of the concerned problem. This transformation is capitalized to extract abundant explicit and analytic solutions. Moreover, Hirota bilinear form of the concerned equation is taken under consideration to discover complexiton solutions via extended transform rational function approach. 3D visualization of the acquired solutions is also included to discuss its physical behavior. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to implement the collective variable method to investigate the generalized complex Ginzburg–Landau equation, which characterizes the kinetics of solitons in respect of pulse parameters for fiber optics. The statistical simulations of the interacting system of ordinary differential equations that reflect all the collective variables included in the pulse ansatz have been successfully carried out using a well-known numerical methodology, the fourth-order Runge–Kutta technique. The collective variable method is employed to plot the pulse variation characteristics as a function of propagation distance. The amplitude, temporal position, width, chirp, frequency, and phase of the pulse are all depicted against the propagated coordinate, where the width, phase of soliton, amplitude, and chirp all show a strong periodicity. The numerical dynamics of solitons have also been exhibited against varying values of pulse parameters to highlight differences in collective variables. Other key bits of the current investigation are also determined. [ABSTRACT FROM AUTHOR]

This paper reveals optical soliton solutions to fiber Bragg gratings (FBGs) with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are no doubt a technological spectacle that sustained balance between dispersion and the nonlinear effects that leads to a stable transmission of solitons across intercontinental distances. FBGs as sensor elements are used for measuring numerous engineering parameters such as temperature, strain, pressure, tilt, displacement, acceleration, load. Two recently developed mechanisms such as the unified method and extended sinh-Gordon equation expansion method (ShGEEM) are successfully employed to secure optical pulses in the shapes of the bright, dark, singular, complex combo, periodic, and plane wave solutions. The achieved solutions contain key applications in engineering and physics. These solutions define the wave performance of the governing models. By selecting suitable parametric values, the dynamics of the evaluated results are exemplified by sketching their 2-dimensional, 3-dimensional, and contour profiles to understand the real phenomena for such sort of nonlinear models. The novelty of the gained outcomes is manifested by a detailed comparison with the results that already exist. [ABSTRACT FROM AUTHOR]

The integrable Lakshmanan–Porsezian–Daniel (LPD) equation originating in nonlinear fiber is studied in this work via the Riemann–Hilbert (RH) approach. First, we give the spectral analysis of the Lax pair, from which an RH problem is formulated. Afterwards, by solving the special RH problem with reflectionless under the conditions of irregularity, the formula of general N -soliton solutions can be obtained. In addition, the localized structures and dynamic behaviors of the breathers and solitons corresponding to the real part, imaginary part and modulus of the resulting solution r (x , t) are shown graphically and discussed in detail. Unlike 1- or 2-order breathers and solitons, 3-order breathers and soliton solutions rapidly collapse when they interact with each other. This phenomenon results in unbounded amplitudes which imply that higher-order solitons are not a simple nonlinear superposition of basic soliton solutions. [ABSTRACT FROM AUTHOR]

In this paper, an N -coupled high-order nonlinear Schrödinger system, which describes the properties of the ultrashort optical pulses in an optical fiber, is investigated with the Darboux transformation (DT) method and asymptotic analysis. Starting from the given (2 N + 1) th-order Lax pair, we construct a new form of the DT (with some complex eigenfunctions of a Lax pair involved) to derive the formulas of the n th-iterated solutions, where n and N are the positive integers. On the zero background, the first- and second-order solitons are obtained and analyzed through the asymptotic analysis. Multi-parameter adjustment is proceeded since there are 3 N + 4 real parameters in the second-order solitons. We find that under certain conditions each of the two interaction patterns (elastic and/or inelastic) holds in the second-order solitons. On the plane wave background, the first-order bright and dark–bright solitons are obtained. Velocities, amplitudes, widths and characteristic lines of the first-order bright and dark–bright solitons are presented and analyzed. [ABSTRACT FROM AUTHOR]

This research is about some new exact solitons to the new Hamiltonian amplitude equation with novel truncated M-fractional derivatives. Extended Sinh-Gordon equation expansion method (ShGEEM) is applied to obtain solitons to the new Hamiltonian amplitude equation with novel truncated M-fractional derivatives. The obtained results may be used in the description of the model in a fruitful way. The novel derivative operator is applied to study the aforementioned model. The achieved results are in the form of dark, bright, and combo optical solitons. The achieved solutions are also verified by using the Mathematica software. Some of the solutions are drawn in two and three dimensions so that the results can be easily discussed through them. [ABSTRACT FROM AUTHOR]

In this paper, modified equal width Burgers' equation has been investigated with the aid of unified method and bifurcation. This model has many applications in long wave transmission with dispersion and dissipation in nonlinear medium. The applied technique is efficient to retrieve exact solutions and their dynamic behaviors. The obtained solutions are polynomial and rational function solutions. The behavior of dynamical planer system has been analyzed by assigning different values to the parameters, also each possible case has been shown as phase portraits in this research paper. The estimated solutions demonstrate that the proposed approaches are simple, practical, and promising for investigating further equal width equation's soliton wave solutions and phase portraits. [ABSTRACT FROM AUTHOR]

In this research paper, we scrutinize the novel traveling wave solutions and other solutions with conformable, M-truncated and beta fractional derivatives for the nonlinear fractional Hirota–Maccari system. In order to acquire the analytical solutions, the Riccati–Bernoulli sub-ODE technique is implemented. Presented method is the very powerful technique to get the novel exact soliton and other solutions for nonlinear partial equations in sense of both integer and fractional-order derivatives. Mathematical properties of different kinds of fractional derivatives are given in this paper. A comparative approach is presented between the solutions with the fractional derivatives. For the validity of the solutions, the constraints conditions are determined. To illustrate the physical meaning of the presented equation, the 2D and 3D graphs of the acquired solutions are successfully charted by selecting appropriate values of parameters. [ABSTRACT FROM AUTHOR]

In this paper, we consider (2 + 1) and (3 + 1) -dimensional Boiti–Leon–Manna–Pempinelli equations. We obtain the soliton solutions by using the new extended direct algebraic method. The resulting solutions carry a variety of new families including the singular solution of type 1 and 2, dark, dark-bright, and dark-singular soliton solution. These solutions contain trigonometric, hyperbolic, and exponential type functions. Moreover, to highlight the important features of the obtained solutions, some three-dimensional and two-dimensional diagrams of these solutions are plotted with the suitable choice of the values of the involving parameters. [ABSTRACT FROM AUTHOR]

This research finds an equation in a continuous domain and a discrete equation governing the system of cold bosonic atoms (CBA) in a zigzag optical lattice using a continuum approximation. Many solutions to the equation were obtained using two distinct methods: the three-wave approach (multi-wave interaction, rational solutions, and rational solution interaction) and the extended sub-equation method. These analytical approaches are more effective, consistent, and comprehensive mathematical tools for obtaining various exact closed-form solutions for a wide range of fractional space-time nonlinear evolution equations encountered in optical physics, condensed matter physics, and plasma physics. The solutions generated are in the form of hyperbolic and trigonometric solutions, and other-form solutions are obtained. Three-dimensional graphics and contour plots are often used to depict the graphical representations of the combined soliton solutions. These findings will aid our understanding of the dynamics of the zigzag optical grids and many other structures formed by colder bosonic atoms. The applied approaches are more simple, efficient, and straightforward to obtain the closed-form solutions for various nonlinear evolution equations in the fields of nonlinear sciences and physical engineering. [ABSTRACT FROM AUTHOR]

In this paper, we pay attention to the nonlinear dynamical behavior of ultra-short pulses in optical fiber. The new Hamiltonian amplitude equation is used as a governing model to analyze the pulses. We secure the ultra-short pulses in the forms of bright, dark, singular, combo and complex soliton solutions by the utilization of three of sound computational integration techniques that are protracted (or extended) Fan-sub equation method (PFSEM), the generalized exponential rational function method (GERFM), extended Sinh-Gordon equation expansion method (ShGEEM). Moreover, Jacobi's elliptic, trigonometric, and hyperbolic functions solutions are also discussed as well as the constraint conditions of the achieved solutions are also presented. In addition, we discuss the different wave structures by the assistance of logarithmic transformation. The findings demonstrate that the examined equation theoretically contains a large number of soliton solution structures. By selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in 3D and 2D profiles. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex phenomena. The resulting solutions are novel, intriguing, and potentially useful in understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including nonlinear optics. Our new results have been compared to these in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to compute solitary wave solutions and soliton wave solutions based on the ansatz methods to the perturbed nonlinear Schrödinger equation (NLSE) arising in nano-fibers. The improved tan (/ 2) -expansion method and the rational extended sinh–Gordon equation expansion method are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accuracy interpretation of the propagation of solitons. We held a comparison between our results and those are in the previous work. The outcome indicates that perturbed NLSE arising nano-fibers is used in optical problems. Finally, via symbolic computation, their dynamic structure and physical properties were vividly shown by three-dimensional, density, and t -curves plots. These solutions have greatly enriched the exact solutions of (2+1)-dimensional perturbed nonlinear Schrödinger equation in the existing literatures. [ABSTRACT FROM AUTHOR]

In this article, the space-time fractional perturbed nonlinear Schrödinger equation (NLSE) in nanofibers is studied using the improved tan (ϕ (ξ) / 2) expansion method (ITEM) to explore new exact solutions. The perturbed nonlinear Schrodinger equation is a nonlinear model that occurs in nanofibers. The ITEM is an efficient method to obtain the exact solutions for nonlinear differential equations. With the help of the modified Riemann–Liouville derivative, an equivalent ordinary differential equation has been obtained from the nonlinear fractional differential equation. Several new exact solutions to the fractional perturbed NLSE have been devised using the ITEM, which is the latest proficient method for analyzing nonlinear partial differential models. The proposed method may be applied for searching exact travelling wave solutions of other nonlinear fractional partial differential equations that appear in engineering and physics fields. Furthermore, the obtained soliton solutions are depicted in some 3D graphs to observe the behaviour of these solutions. [ABSTRACT FROM AUTHOR]

In this work, the new optical soliton solutions and interaction solutions for the space-time fractional Fokas–Lenells equation with fractional M -derivatives are constructed via three mathematical analytical techniques, namely the extended SE method, unified solver method, and three-wave methods. The results have proved the efficiency of the suggested techniques for obtaining abundant optical soliton solutions to nonlinear evolution equations (NLEEs) and closed-form solutions in the forms of rational function solutions; hyperbolic and trigonometric function solutions and multi-wave interaction solutions are obtained. These techniques are more efficient, robust, and powerful mathematical tools for acquiring several optical soliton solutions for many other fractional space-time NLEEs that arise in optical physics and plasma physics. The graphical representations of the combined optical solitons are demonstrated using three- and two-dimensional graphics. [ABSTRACT FROM AUTHOR]

This paper comprises the different types of optical soliton solutions of an important Triki–Biswas model equation with beta-time derivative. The beta derivative is considered as a generalized version of the classical derivative. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation that describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel beta derivative operator and three efficient integration schemes. During this work, a sequence of new optical solitons is produced that may have an importance in optical fiber systems. These solutions are verified and numerically simulated through soft computation. [ABSTRACT FROM AUTHOR]

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations. [ABSTRACT FROM AUTHOR]

In the current analysis, the conformable generalized Kudryashov equation of pulses propagation with power non-linearity is processed. The considered higher order equation represents a generalized mathematical model of many well-known ones in nonlinear media. A variety of multiple kinks, bi-symmetry, periodic, singular, bright and dark optical solitons are extracted via the generalized Riccati equation mapping method. Basing on the Riccati differential equation, the theoretical algorithm extracts a number of empirical solutions that do not exist in the literature. The obtained results showed that the present technique is an effective and strong tool for solving nonlinear fractional partial differential equations and produces a very large number of solutions. [ABSTRACT FROM AUTHOR]

This paper presents new optical solitons of a fractal Fokas–Lenells equation that models the dynamics of optical fibers. The Painlevé technique is employed to identify kink soliton solutions. The constraint conditions guarantee the existence of these solitons. The outcomes of this research give new solutions that are not achieved using some already defined algorithms. The derived method is efficient and its applications are promising for other nonlinear problems. The 3D graphical illustrations of obtained results are depicted for various values of the fractal parameter. [ABSTRACT FROM AUTHOR]

In this paper, we study (2+1)-dimensional non-linear spin dynamics of Heisenberg ferromagnetic spin chains equation (HFSCE) for various soliton solutions. We obtain two types of optical solitons i.e. chirp free and chirped solitons. We obtain bright and bright-like soliton, singular-like solitons, periodic and rational solutions, Weierstrass elliptic functions solutions and other solitary wave solutions for HFSCE with the aid of sub-ODE method. At the end, we present graphical representation of our solutions. [ABSTRACT FROM AUTHOR]

In this article, we investigate the optical soiltons and other solutions to Kudryashov's equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as Φ 6 -model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]

This article investigates the optical solitons to the three coupled Gross–Pitaevskii (GP) system (also called the non-linear Schrödinger (NLS) equation), which describes the F = 1 spinor Bose–Einstein condensate, with F denoting the atom's spin. The solutions are expressed in the form of hyperbolic function solutions that have different physical meanings such that the hyperbolic tangent appears in the calculation and rapidity of special relativity while, the hyperbolic cotangent arises in the Langevin function for magnetic polarization, the hyperbolic secant arises in the profile of a laminar jet. The various kinds of soliton solutions in single and combined form like bright, dark, singular as well as bright-dark and singular in the mixed form are also extracted by the mean of extended sinh-Gordon equation expansion method. By using the appropriate values of the involved parameters, 3D, 2D and their corresponding contour graphs are sketched for physical movement of the attained results. We also discuss the modulation instability (MI) analysis of the governing model. The constraint conditions for the existence of soliton solutions are also mentioned. The calculated work and earned results show the power, effectiveness, and the simplicity of applied method to discuss the soliton solutions as the contrast with other analytical schemes. The main outcome of the proposed technique is that we have succeeded in a single move to get and organize various types of new solutions. [ABSTRACT FROM AUTHOR]

The Fokas–Lenells (FL) equation is analyzed in this paper as an ironic physical function in optical fibers. A class of FL-equation soliton solutions is constructed by He's variational principle. Besides, the fractal model of FL and its theory of variation are established. This paper focuses on the innovative research frontiers of FL equation. [ABSTRACT FROM AUTHOR]

Under investigation in this paper is the dynamics of dispersive optical solitons modeled via the Schrödinger–Hirota equation. The modulation instability of solutions is firstly studied in the presence of a small perturbation. With symbolic computation, the one-, two-, and three-soliton solutions are obtained through the Hirota bilinear method. The propagation and interaction of the solitons are simulated, and it is found the collision is elastic and the solitons enjoy the particle-like interaction properties. In the end, the asymptotic behavior is analyzed for the three-soliton solutions. [ABSTRACT FROM AUTHOR]

This paper studies the Biswas–Arshed model that compensates for the group velocity dispersion (GVD) by the dispersion of time and space. When the GVD and non-linearity are very small, the propagation patterns of the model are given by the complete discriminant system for polynomial method. Based on the results, under the specific parameters, we analyze the soliton transmission dynamic. [ABSTRACT FROM AUTHOR]

The study focuses on the use of a direct algebraic approach to the analysis of the Triki–Biswas (TB) model. This model addresses the distribution of ultrashort pulses in optical fiber in the presence of non-Kerr dispersion concept and group velocity dispersion. However, using the new extended direct algebraic method, we have obtained various optical soliton solutions for the TB model. The optical soliton solutions are new and reliable compared to the existing methods. [ABSTRACT FROM AUTHOR]

In this work, we investigate the perturbed optical solitons to the Gerdjikov-Ivanov equation consisting of group velocity dispersion and quintic nonlinearity coefficients, which communicate the propagation of pulses in nonlinear optics. The various kinds of solitons in single and combined forms like dark, singular, dark-singular, bright-dark are derived by Fan-extended sub equation method. Moreover, the singular periodic, triangular type solutions are also obtained. And, we also discuss the stability analysis of the studied nonlinear model with the concept of linear stability, we prove that the governing model is stable. Parametric conditions on physical parameters to ensure the existence criteria of optical solitons are also listed. We also plot 3D profiles for the physical behavior of the obtained solutions by selecting the suitable values of the parameters. [ABSTRACT FROM AUTHOR]

This paper deals with the study of optical solitons in the presence of new linear and nonlinear parity-time (𝒫 𝒯) -symmetric modulation lattices. The nonlinear medium is a derivative term with arbitrary power. Inverse engineering scheme is utilized to retrieve bright, dark, dipole and singular soliton solutions. These solutions are presented for four new 𝒫 𝒯 -symmetric potentials. The results reveal that optical bright, dark and dipole solitons can exist for those new physical settings. [ABSTRACT FROM AUTHOR]

The extended generalizing Riccati mapping method (EGRM) is used to solve the derivative nonlinear Schrödinger equation (DNLSe) with the dimensionless shape. This method reveals several optical solitons including traveling wave solutions (TWS). The studied solutions are identified in four different families including the hyperbolic, the rational and the trigonometric functions. Evaluations of the method are presented with graphical results obtained from our solutions. [ABSTRACT FROM AUTHOR]

The Kundu–Mukherjee–Naskar model is studied to reveal some vital optical solitons in (2 + 1) dimensions. To obtain singular soliton, dark soliton, combined dark-singular soliton and other hyperbolic solutions, we will use csch method, extended Tanh–Coth method and extended rational sinh-cosh method receptively with constraint conditions. [ABSTRACT FROM AUTHOR]

An integrable extension of the famous Schrödinger equation in (2 + 1) dimension, named Kundu–Mukherjee–Naskar (KMN) equation, governing the evolution of ion-acoustic wave in magnetized plasma and oceanic rogue waves is considered, and dark/black as well as gray optical soliton solutions are constructed by using a complex envelope ansatz approach with appropriate conditions for the existence of solitons. Also, a new class of combined gray and black optical soliton solutions is obtained by applying Chupin Liu's theorem, and it is found to be anti-dark solitons. Additionally, Gaussian wave solutions are derived. Further, the investigation of symmetry analysis, nonlinear self-adjointness and conservation laws (Cls) for the KMN equation are carried out. These results further enrich and deepen the understanding of the dynamics of a higher-dimensional soliton propagation. [ABSTRACT FROM AUTHOR]

In this paper, the modulation instability (MI) of a (1 + 1) -dimensional nonlocal nonlinear Schrödinger equation with general polynomial law nonlinearity and an external potential is investigated. Some new dark and bright soliton solutions are obtained for polynomial law nonlinearities of third and fifth orders. [ABSTRACT FROM AUTHOR]

The model of optical propagation in nonlocal parabolic law medium is described by nonlinear Schrödinger equation with high-order nonlinear terms. Exact optical propagation patterns are constructed by proposing a general complex trial equation method. These results show rich optical propagation patterns of the model. [ABSTRACT FROM AUTHOR]

Kerr media are applied in the photonic lattices and optical fibers, while optical fiber communication becomes one of the main pillars of modern communication. In this letter, we study a (3 + 1)-dimensional nonlinear Schrödinger equation with distributed coefficients for the spatiotemporal optical solitons or light bullets in a diffractive nonlinear Kerr medium with anomalous dispersion. The N-dark soliton solutions in terms of the Gramian is obtained via the Kadomtsev–Petviashvili hierarchy reduction, where N is a positive integer. Via the graphic analysis, we observe the interaction of the two dark solitons. Effects from the diffraction/dispersion coefficient β (z) and gain coefficient γ (z) are also discussed on the amplitudes and oscillations of the two dark solitons, as well as on the interaction of the two dark parabolic shape solitons. [ABSTRACT FROM AUTHOR]

Exact envelop patterns of nonlinear Schrödinger equation (NLSE) with perturbation terms are constructed to describe optical solitons in quadratic-cubic nonlinear medium by proposing a complex version of Liu's trial equation method. These four families of envelop solutions show various properties of patterns of amplitudes including singularity, periodicity and double periodicity. [ABSTRACT FROM AUTHOR]

We consider a generalized fourth-order nonlinear Schrödinger (NLS) equation. Based on the ansatz method, its bright, dark single-soliton is constructed under some constraint conditions. Furthermore, combining the Riccati equation extension approach, we also derive some exact singular solutions. With several parameters to play with, we display the dynamic behaviors of bright, dark single-soliton. Finally, the condition for the modulational instability (MI) of continuous wave solutions for the equation is generated. It is hoped that our results can help enrich the nonlinear dynamics of the NLS equations. [ABSTRACT FROM AUTHOR]

This paper discusses bright, dark and singular optical soliton as well as complexiton solutions to the coupled Fokas–Lenells equation (FLE) for birefringent fibers by three integration tools such as exp (− ϕ (χ)) -expansion method, the first integral method and the sine-Gordon expansion method. The existence criterion of these solutions is also given. [ABSTRACT FROM AUTHOR]

In this paper, we have established the new exact solitons solutions of the nonlinear Biswas–Arshed equation which are used to study soliton dynamics in optical fibers, pivotal cloud foundry (PCF) and metamaterials via the prominent approach, known as auxiliary equation method. The obtained solutions disclosed that the suggested method is the essential addition for studying the exact solution of nonlinear Biswas–Arshed equation. [ABSTRACT FROM AUTHOR]

This paper retrieves chirped sub-pico optical pulses for Triki–Biswas equation with the help of two integration architectonics. This model discusses ultrashort pulses propagation in optical fiber in the presence of non-Kerr dispersion term and group velocity dispersion. We will obtain bright, dark and dark singular combo-optical solitons under some constraint conditions. [ABSTRACT FROM AUTHOR]

In this study, two integration techniques are employed to reach optical solitons to the (n + 1) -dimensional nonlinear Schrödinger's equation ((n + 1) -NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamics of optical solitons in nonlinear Schrödinger equation (NLSE) with cubic-quintic law nonlinearity in the presence of self-frequency shift and self-steepening. This type of equation describes the ultralarge capacity transmission and traveling of laser light pulses in optical fibers. Two robust analytical approaches are employed to determine contemporary solutions. Some new explicit rational, periodic and combo periodic soliton solutions are extracted using the extended trial equation method. The Riccati–Bernoulli sub-ODE method provided us with singular and dark soliton solutions. The constraints found are necessary for the existence of solitons. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of cubic–quartic NLSE with the Kerr law nonlinearity via a new sub-equation method. Considered method of undetermined coefficients is applied to obtain the introduced solutions. The outcomes are useful in describing the diffusion of optical solitons. The performance of the approach is reliable, useful and gives more new general exact solutions than the other methods. [ABSTRACT FROM AUTHOR]

In this paper, we discussed analytically higher order dispersive extended nonlinear Schrödinger equation with the aid of newly developed technique named as extended modified auxiliary equation mapping method. As a result, we have found a variety of new families of exact traveling wave solutions including bright, dark, half-bright, half-dark, combined, periodic, doubly periodic, with the help of three parameters, which is the key importance of this method. For physical description of our newly obtained solutions, we have expressed them graphically using Mathematica 10.4 to explain more efficiently the behavior of different shapes of solutions. [ABSTRACT FROM AUTHOR]