Optical Soliton Solutions Research Articles

New optical soliton solutions to the (n+1) dimensional time fractional order Sinh-Gordon equation

This article studies and constructs new optical soliton solutions for the (n+1)-dimensional time fractional order Sinh-Gordon equation. First, we change the differential equation into Ordinary differential equation which is connected with a quartic polynomial based on traveling wave transformation. Then using the polynomial complete discrimination system to classify the roots of the fourth degree polynomial, the exact solutions of the Sinh-Gordon equation are classified, and these specific expressions of optical soliton solutions are given. This solution process is simple, fast, and very effective. The characteristics of some exact solutions were given using 3D, 2D, and contour graphs, which help researchers gain a deeper understanding of the physical characteristics corresponding to the model which we discuss in this article.

Optical soliton solutions and dynamical behaviours of Kudryashov’s equation employing efficient integrating approach

Optical soliton solutions and dynamical behaviours of Kudryashov’s equation employing efficient integrating approach

Exact Optical Solitons for Generalized Kudryashov’s Equation by Lie Symmetry Method

In this article, we use Lie point symmetry analysis to extract some new optical soliton solutions for the generalized Kudryashov’s equation (GKE) with an arbitrary power nonlinearity. Using a traveling wave transformation, the GKE is transformed into a nonlinear second order ordinary differential equation (ODE). Using Lie point symmetry analysis, the nonlinear second-order ODE is reduced to a first-order ODE. This first-order ODE is solved in two cases to retrieve some new bright, dark, and kink soliton solutions of the GKE. These soliton solutions for the GKE are obtained here for the first time.

New optical soliton solutions to the coupled fractional Lakshmanan–Porsezian–Daniel equations with Kerr law of nonlinearity

This article studies the optical soliton solutions of the coupled fractional Lakshmanan–Porsezian–Daniel equations with kerr’s law nonlinearity based on the complete discriminant system of cubic polynomials. By means of traveling wave transformation, the fractional Lakshmanan–Porsezian–Daniel equations are simplified into two ordinary differential equations. Then, according to the classification of the roots of cubic polynomials, the optical soliton solutions of the fractional model with Kerr’s law nonlinearity are traversed. Then new traveling wave solutions are obtained, including the rational solutions, triangle function solutions, implicit function solutions and Jacobian elliptic function solutions, and the corresponding solutions are shown in two-dimensional and three-dimensional figures. Compared with previous related research, the exact optical soliton solutions of the LPD equation system for nonlinear Kerr’s law presented in this study are more completely and clearly classified, and researchers are easier to obtain these solutions.

Dynamical structure of optical soliton solutions for M−fractional paraxial wave equation by using unified technique

This study deliberates the fractional form of the paraxial wave equation, which is used to investigate the self-focusing of optical waves in nonlinear media. The truncated time M−fractional derivative is used to get rid of the fractional order in the governing model. The several optical wave pattern of the paraxial wave equation can play an insignificant role to describe the dynamics of optical soliton solutions in optics and photonics for the study of various physical processes, including the propagation of light through optical systems, such as lenses, mirror, and fiber optics. In this framework, the newly introduced unified scheme is implemented to investigate optical soliton solutions of truncated time M−fractional Paraxial Wave (tM-fPW) equation. Under some conditions, the established solutions are expressed in terms of hyperbolic, trigonometric, and rational function forms with some free parameters. For the numerical values of the free parameters, we found optical periodic wave, the interaction of periodic wave and rogue wave, breather wave, linked rogue wave, periodic rogue wave solution, etc. For a corporeal explanation of the obtained solutions, we plotted among them with 3-D, density, and contour plots and analyzed the self-focusing of an optical pulse in nonlinear media.

Optical soliton solutions of dispersive Schrödinger–Hirota equation with chromatic and inter-modal dispersion in a couple of law medium

Optical soliton solutions of dispersive Schrödinger–Hirota equation with chromatic and inter-modal dispersion in a couple of law medium

On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods

On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods

Optical soliton solutions, bifurcation, and stability analysis of the Chen-Lee-Liu model

The Chen-Lee -Liu model has many applications in assorted fields, particularly in the study of nonlinear dynamics, chaos theory, circuit design, signal processing, secure communications, encryption and decryption of chaotic signals, as well as cryptography. The modified extended auxiliary equation mapping method has been applied to the Chen-Lee-Liu model in this article and explores new wave profiles, such as singular periodic solutions, periodic solutions, and kink-type soliton solutions. The complex wave conversion is considered to make a simple differential equation. Three- and two-dimensional images are plotted using Mathematica and MATLAB, and their dispersion and nonlinearity effects are discussed. We also discuss the bifurcation analysis of the studied model. The stability of the equilibrium points is studied, and the phase portrait of the system is presented graphically. The obtained wave profiles might play an important role in telecommunication systems, fiber optics, and nonlinear optics.

New optical soliton solutions and dynamical wave formations for a fractionally perturbed Chen-Lee-Liu (CLL) equation with a novel local fractional (NLF) derivative

In this work, we use a novel fractional-order derivative for the fractionally perturbed Chen–Lee–Liu nonlinear equation. The new extended hyperbolic function (EHF) method is applied for obtaining new optical soliton solutions of the mentioned equation. Three-dimensional graphics and projection 3D plots are used for showing the dynamic wave formations of the soliton solutions. Then, we contrast our findings with the earlier existing results for the nonlinearly perturbed CCL. The generated solutions show that the extended hyperbolic function (EHF) method for finding soliton solutions to highly nonlinear equations is productive, suitable, and competent in optical fibers, fractional calculus, and nonlinear sciences.

On the dynamics of a dual space–time fractional nonlinear Schrödinger model in optical fibers

The nonlinear Schrödinger equation (NLSE) is a significant nonlinear complex model known as the most important struture to represent light pulse propagation in optical fibers, which plays a key role in demonstrating the proliferation specifically short pulse in optical fibers and have large appliances in telecommunication system and ultra fast signal routing in nonlinear optics. In this study, we look into explicit solutions of a coupled fractional NLSE for a dual space–time, which reflect numerous explicit travelling wave solutions, as well as their physical interpretation. We use the fractional complex transform to obtain multiple exact answers using the unified technique and the extended simple equation method. These exact answers include trigonometric function solutions as well as dark, bright, singular, periodic, and optical soliton solutions. For a set of appropriate parameters, Mathematica is used to represent the dynamics of various wave structures as 3D, 2D, and contour visualizations. These findings show that the proposed methodologies are simple, prolific, and capable of studying the nature of numerous physical models of complex phenomena in modern science.

Parametric effects on paraxial nonlinear Schrödinger equation in Kerr media

• The mentioned techniques are applied to the paraxial NLS equation in Kerr media. • Optical soliton solutions are obtained and has parameters connected to the model. • Analyzed the nature of the obtained solutions by 3D and 2D wave profiles. • Nonlinear and free parameters effects on the paraxial NLS equation have been analyzed. • Wave profiles streamline pattern and immediate local directions have been analyzed. In this study, we have considered the (2+1)-dimensional paraxial nonlinear Schrödinger (NLS) equation in Kerr media and used the ( w / g ) - expansion method. The g ′ and ( g ′ / g 2 ) -expansion techniques have been customized from the ( w / g ) - expansion method. We applied these two techniques to the paraxial NLS equation and found the optical soliton solutions. The optical soliton solutions are attained as the flat kink, kink, singular kink, peakon, anti-parabolic, W-shape, M-shape, bell, and periodic wave solitons in terms of free parameters. We have presented three-dimensional (3D), two-dimensional (2D) and contour plots of the obtained results and discussed the effect of the free parameters and nonlinearity of the equation by determining different parametric values, which have not been discussed in the previous literature. We have studied the impact of the Kerr nonlinearity and wavenumber on the travelling wave solutions. Moreover, we also analyze the streamlines pattern and instantaneous local directions of the wave profile. All wave phenomena are applied to signal transmission, magneto-acoustic waves in plasma, optical fiber art, coastal engineering, quantum mechanics, hydro-magnetic waves, nonlinear optics and so on. The achieved solutions prove that the proposed methods are very powerful and effective for modern science and engineering for scrutinizing nonlinear evolutionary equations.

Optical Solitary Waves and Soliton Solutions of the (3+1)-Dimensional Generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony Equation

Optical Solitary Waves and Soliton Solutions of the (3+1)-Dimensional Generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony Equation

OPTICAL SOLITARY WAVES AND SOLITON SOLUTIONS OF THE (3 + 1)-DIMENSIONAL GENERALIZED KADOMTSEV–PETVIASHVILI–BENJAMIN–BONA–MAHONY EQUATION

In this investigation, an appropriate traveling wave transformation has been employed to analyze the fourth-order nonlinear (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation for an offshore structure. In addition to being integrable and having constant coefficients, the examined model represents fluid flow in the context of an offshore structure. The aforesaid nonlinear system is subjected to the initial application of two trustworthy and dependable approaches, namely the improved Bernoulli sub-equation function method and the modified extended-function method. Investigating and obtaining certain explicitly exact traveling waves, periodic waves, and soliton solutions is the major objective. The generated solutions take the form of trigonometric hyperbolic functions, exponential functions, rational functions, and multiple forms of trigonometric functions. The proposed solutions are both novel and important in that they provide light on the relevant aspects of the physical phenomena. The characteristics of the solutions have been displayed in a variety of figures, including two- and three-dimensional ones, for the best visual optical discernment.

Optical soliton solutions for time-fractional Fokas system in optical fiber by new Kudryashov approach

Optical soliton solutions for time-fractional Fokas system in optical fiber by new Kudryashov approach

Discovering optical soliton solutions in the Biswas–Milovic equation through five innovative approaches

Purpose:In recent years, depending on the development of models containing highly dispersive nonlinear equations, especially in the field of nonlinear optics, it has been important to obtain the solutions of these equations with analytical methods. This study presents some effective, reliable, and easily applicable solution techniques based on the well-known extended auxiliary equation. Besides, these techniques were applied to the Biswas–Milovic equation. Methodology:First, in order to achieve the ordinary differential equation structure of the Biswas–Milovic equation, the complex wave transform was given and utilized. Then, the algorithms, constraints of each proposed approach, and key points for their implementation were presented. In addition, the relations and transitivities between the methods are also interpreted. Second, analytical optical soliton solutions were obtained by applying the proposed techniques. Lastly, graphical simulations of optical soliton types represented by some solution functions are made. Findings:It has been shown that all of the proposed methods yield effective results in solving the Biswas–Milovic equation and can be used not only for nonlinear evolution equations but also for highly dispersive nonlinear optical equations. It has been observed that the methods have the capacity to be employed easily and do not require tedious calculus and algebraic manipulations. Originality:The work in the article has not been presented before.

Optical Solitons and Modulation Instability Analysis with Lakshmanan–Porsezian–Daniel Model Having Parabolic Law of Self-Phase Modulation

This paper seeks to find optical soliton solutions for Lakshmanan–Porsezian–Daniel (LPD) model with the parabolic law of nonlinearity. The spatiotemporal dispersion is included to the model, as it can contribute to handling the problem of internet bottleneck. This study was performed analytically using the traveling wave hypothesis to reduce the model to an integrable form. Then, the resulting equation was handled with two approaches, namely, the auxiliary equation method and the Bernoulli subordinary differential equation (sub-ODE) method. With an intentional focus on hyperbolic function solutions, abundant optical soliton waves including W-shaped, bright, dark, kink-dark, singular, kink, and antikink solitons were derived with the existing conditions. Furthermore, the behaviors of some optical solitons are illustrated. The spatiotemporal dispersion was found to significantly affect the pulse propagation dynamics. Finally, the modulation instability (MI) of the LPD model is explained in detail along with the extraction of the expression of MI gain.

Highly dispersive optical solitons in fiber Bragg gratings with stochastic perturbed Fokas–Lenells model having spatio-temporal dispersion and multiplicative white noise

In this paper, we derive optical soliton solutions with highly dispersive optical solitons in fiber Bragg gratings with stochastic perturbed Fokas–Lenells model having spatio-temporal dispersion and multiplicative white noise. In this regard, we have applied two effective methods of distinct analytical mathematical methods to find explicit solutions to many physical and engineering problems, namely addendum Kudryashov’s (AK’s) method and the unified Riccati equation expansion method (UREEM). Bright soliton, Straddled solitary solutions, singular solitons, dark soliton are acquired.

Optical soliton solutions to the space–time fractional perturbed Schrödinger equation in communication engineering

Optical soliton solutions to the space–time fractional perturbed Schrödinger equation in communication engineering

New optical soliton solutions for the (2+1) Fokas system via three techniques

New optical soliton solutions for the (2+1) Fokas system via three techniques

New optical soliton solutions of thin-film ferroelectric material equation via the complete discrimination system method

In this paper, our main aim is to construct the optical soliton solutions of the well-known thin-film ferroelectric material equation, which describes the propagation of polarization in thin-film materials. Because it has been found that solitary waves may be important for the propagation of polarization fields in ferroelectrics, we investigate its optical soliton solutions using the complete discrimination system technique in this study. As a result, the optical soliton solutions and various solutions are acquired, covering the elliptic double periodic function solution, Jacobian elliptic function solution etc. It appears that bright and singular waves can be propagated in thin-film ferroelectric materials. The richness of the solutions obtained will be conducive to further understand the whole picture of the dynamic behavior of wave propagation in thin-film material. Moreover, this research methods and results are efficacious and can be applied to the exploration of more complex phenomena. Finally, via giving some fixed parameter values, we plot 3D, 2D, density and contour graphs of some obtained solutions for presenting in visual form.