Optical Soliton Solutions Research Articles

Optical soliton solutions of the perturbed Fokas–Lenells equation

This paper investigates the Fokas–Lenells equation with perturbation terms in optical soliton dynamics, which describes the propagation of a pulse in a single-mode fibre. A rich set of single travelling wave solutions to this equation, including some new solutions, is obtained by direct integration methods. The dynamical properties of these solutions are discussed using qualitative analysis theory. These solutions help us better understand the model’s dynamic behaviour and further illustrate its nature.

The investigation of unique optical soliton solutions for dual-mode nonlinear Schrödinger’s equation with new mechanisms

The investigation of unique optical soliton solutions for dual-mode nonlinear Schrödinger’s equation with new mechanisms

Optical soliton solutions for the integrable Lakshmanan-Porsezian-Daniel equation via the inverse scattering transformation method with applications

The Lakshmanan-Porsezian-Daniel equation (LPD) is a nonlinear Schrödinger type (NLS) equation which describe the effect on the integrable properties of Heisenberg bilinear spin chains under the classical limit by the biquadratic interactions. In this paper, the integrability of LPD equation is illustrated by obtaining the Lax pair via the AKNS scheme. The exact soliton solutions via the inverse scattering transformation (IST) method are obtained and illustrated in 3D graphical representation.

Optical solitons to the fractional order nonlinear complex model for wave packet envelope

This research deals with the fractional order nonlinear complex model, which is a general form of nonlinear Schrodinger equation. This model demonstrates boson gas among 2 as well as 3 body collisions, nuclear hydro-dynamics allied with Skyrme energies, in addition the optical rhythm propagations within dielectric non-Kerr media. To analyze and generate complex dynamics, optical soliton solutions of the model are derived through improved generalized Riccati equation mapping scheme. As a result, bright, dark and combo bright-dark optical wave envelopes and oscillating pulse bright optical solitons are obtained. The effects of fractionality and parameters are also illustrated with few numerical graphics of the achieved results. The achieved optical (bright and dark) solitons solutions can be used in signal transmission through optical fiber communications system.

Optical soliton solutions of (1 + 1)- and (2 + 1)-dimensional generalized Sasa–Satsuma equations using new Kudryashov method

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies.

Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers

In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the (2+1)-dimensional Hirota–Maccari system. The (2+1)-dimensional Hirota–Maccari system is a special kind of nonlinear Schrödinger equation (NLSEs) that models the motion of isolated waves localized in a small part of space, and is used in such various fields as fiber optics telecommunication systems, nonlinear optics, plasma physics, and hydrodynamics. In addition, the Hirota–Maccari system defines the dynamical characters of femtosecond soliton pulse propagation in single-mode fibers. Analytical solutions of the model are successfully acquired with the assistance of symbolic computation utilizing these methods. Finally, 3D, 2D, and contour graphs of solutions are depicted at specific values of parameters. It is shown that the new Kudryashov method and the tanh-coth method are uncomplicated, very effective, easily applicable, reliable, and indeed vital mathematical tools in solving nonlinear models.

Dispersive optical solitons in magneto-optic waveguides for perturbed stochastic NLSE with generalized anti-cubic law nonlinearity and spatio-temporal dispersion having multiplicative white noise

Object:The current article studies optical solitons solutions for the dimensionless form of the perturbed stochastic NLSE in magneto-optic waveguides with generalized anti-cubic (GAC) law nonlinearity and spatio-temporal dispersion (STD) having multiplicative noise in the itô sense. Methods:The generalized Jacobi-elliptic function expansion method and the addendum Kudryashov’s method are investigated. Results:The generalized Jacobi elliptic function expansion method secures the Jacobi’s elliptic functions solutions, the dark and singular soliton solutions as long as the Weierstrass elliptic functions solutions and periodic wave solutions. The addendum Kudryashov’s method deduces the combo bright-singular soliton, bright soliton and singular soliton solutions.

Optical solitons and traveling wave solutions for the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms

This work mainly concerned with the optical solitons and other traveling wave solutions for the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms. With the assistance of the second-order and triple-order polynomial complete discriminant system method, we construct a series of optical soliton solutions which include bright soliton solutions, singular soliton solutions, dark soliton solutions, periodic solutions, kink solitary wave solutions, anti-kink solitary wave solutions and some other traveling wave solutions. What is more, numerical simulations are also given to visualize the mechanism of the higher-order nonlinear Schrödinger system by selecting some suitable parameters of optical soliton solutions. Finally, we give the comparison between the obtained works in this paper and other’s results.

Optical solitons in the generalized space–time fractional cubic-quintic nonlinear Schrödinger equation with a [formula omitted]-symmetric potential

In the presence of complexified parity reflection–time reversal (PT)−symmetric Scarff-II potential, we consider the generalized space–time fractional cubic-quintic nonlinear Schrödinger (FCQNLS) equation. By implementing fractal derivative variable transformation, we derive the fractional optical soliton solutions for the considered model. We consider two distinct forms of cubic-quintic nonlinearities, such as (i) focusing cubic-focusing quintic and (ii) defocusing cubic-focusing quintic for deriving the fractional optical soliton solutions. We investigate how modifying the temporal and space fractional-order parameters affects these fractional solitons. Our observations reveal that the rise in fractional-order parameters leads to the desired soliton profiles. We also examine further the effects of potential strengths on the fractional soliton profiles that are obtained.

New optical soliton solutions of Biswas–Arshed equation using the generalised exponential rational function approach and Kudryashov’s simplest equation approach

New optical soliton solutions of Biswas–Arshed equation using the generalised exponential rational function approach and Kudryashov’s simplest equation approach

Phase portraits and optical soliton solutions of coupled Sasa–Satsuma model in birefringent fibers

The main purpose of this paper is to discuss the optical soliton solutions and phase portraits of the coupled Sasa–Satsuma model in nonlinear optics. This model is usually used to describe the propagation of femtosecond pulses in optical fibers. By using traveling wave transformation, the coupled Sasa–Satsuma model is simplified into the coupled nonlinear ordinary differential equations. After that, the coupled nonlinear ordinary differential equations are transformed into two-dimensional planar dynamic system with the Hamiltonian system. According to the bifurcation theory of planar dynamical system, the phase portrait of two-dimensional dynamical system is drawn. What is more, some very important optical soliton solutions are also constructed. In order to explain the propagation of optical solitons, three-dimensional diagrams, two-dimensional diagrams and the contour plots of the obtained solutions are drawn by using Maple software.

Optical solitons for Biswas–Milovic equation using the new Kudryashov’s scheme

Purpose:This study aims to examine the optical soliton solutions of the nonlinear Schrödinger form of the (2+1)-Biswas–Milovic equation with Kerr, power and parabolic law nonlinearity. Methodology:Our method steps are as follows; we have obtained the nonlinear ordinary differential equation (NODE) and constraint relations for each Kerr, power and parabolic law nonlinearity forms of main model by using wave transform. Then we have derived the new Kudryashov method soliton solutions over NODE form and checked the obtained solutions satisfy the nonlinear partial differential equation (NLPDE). Finally, graphic drawings have been created and important comments made on the solution results. Findings:The Forms containing Kerr, power and parabolic law nonlinearity of the (2+1)-Biswas–Milovic equation (BME) have been successfully established. The new Kudryashov method (NKM) has been applied and soliton solutions obtained. It is also shown with graphic presentations that the obtained solutions have the basic soliton shapes which are dark, bright and singular. Originality:The investigation of the Kerr, power and parabolic law nonlinearity forms of the (2+1)-Biswas–Milovic equation is given in this manuscript for the first time.

Optical solitons, multiwave, breather and M-shaped solitons for an nonlinear Schrödinger equation in (2+1)-dimensions with cubic–quintic–septic law

In this paper, we address a newly nonlinear Schrödinger equation (NLSE) in [Formula: see text]-dimensions influenced by cubic–quintic–septic law nonlinearity and spatial dissipations effects. We properly construct the dark and bright optical soliton solutions for our governing model. Furthermore, periodic, other singular solutions, multiwave, homoclinic breather, M-shaped rational and their interaction with kink waves of various structures will be derived. In addition to this, some 3D, 2D and contour profiles will be added to anticipate the wave dynamics.

Application of the unified method to solve the ion sound and Langmuir waves model

We present the unified method and use it to integrate the ion sound and Langmuir waves (ISLW) model to retrieve optical soliton solutions. Some new dynamical optical solitons involving the combo of rational, trigonometric, and hyperbolic function solutions are added in this study. The derived optical soliton solutions display various properties such as beat pattern and oscillation with increasing, decreasing, and simultaneously increasing and decreasing amplitudes. Moreover, kink, dark bell, singular kink, single breather, multiple breathers, dark-, bright-, and dark bright periodic waves are founded. Finally, some dynamical characteristics of the acquired solutions are depicted.

Optical soliton solutions of the Chen–Lee–Liu equation in the presence of perturbation and the effect of the inter-modal dispersion, self-steepening and nonlinear dispersion

Optical soliton solutions of the Chen–Lee–Liu equation in the presence of perturbation and the effect of the inter-modal dispersion, self-steepening and nonlinear dispersion

Bright and dark optical solitons for (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using a variety of distinct schemes

The current study is dedicated to furnish a class of bright soliton and dark soliton solutions for the (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation. In this direction we operate with a variety of schemes to derive a class of bright and dark optical soliton solutions. Moreover, we derive another class of solutions of distinct structures, that include periodic, complex, and exponential solutions. This analysis provides new findings with a variety of optical features.

Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

In this study, we have focused on finding soliton solutions of the cubic–quartic Fokas–Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. The main motivation of this study is to produce new solutions with previously unused methods for data transmission models in fiber optic cables together with the developing technology, which has been used very frequently today. We have used three different efficient analytical methods, namely, the Sinh–Gordon expansion method, enhanced modified extended tanh expansion method and unified Riccati equation expansion method. By modifying our proposed method and using it effectively, we have obtained much more optical solutions. We have supported the results with the 3D surface, 2D and contour plots of the soliton solutions, such as singular, periodic, periodic-singular, dark and M-shaped solitons. The originality of the method we propose is that it has never been used before. With the innovation of the method, we have obtained M-shaped solitons, which are very rarely obtainable in soliton waves. On the other hand, enhanced modified extended tanh expansion method have provided us more extra solutions. As the last and most important part, in order to examine physical behaviors, we have investigated the effect of the coefficient of the fourth order dispersion parameter on wave propagation by presenting the graphical representation.

Optical soliton solutions to the fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations

Optical soliton solutions to the fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations

Invariant optical soliton solutions to the Coupled-Higgs equation

Invariant optical soliton solutions to the Coupled-Higgs equation

Bifurcations and dispersive optical solitons for the cubic–quartic nonlinear Lakshmanan–Porsezian–Daniel equation in polarization-preserving fibers

The main attention of this work is to study the bifurcations and optical solitons for the cubic–quartic nonlinear Lakshmanan–Porsezian–Daniel equation in polarization-preserving fibers. Firstly, the NLLPD equation was converted into an equivalent ordinary differential traveling wave system by using the traveling wave transformations. Then, we derive the system’s Hamiltonian and orbits phase portraits. In addition to, we construct dark and singular solitons of this model by using the bifurcation theory of dynamical system method. As you can see, some other dispersive optical solitons have been deduced via the complete discriminant system technique and symbolic computation. It is notable that we give the classification of single traveling wave solutions for NLLPD model at the same time. The obtained conclusions may improve or complement previous conditions. Lastly, in order to further explore the propagation of NLLPD model in nonlinear optics, two-dimensional and three-dimensional graphs are drawn by selecting appropriate parameters of the optical soliton solutions.