Radhakrishnan Kundu Lakshmanan Equation Research Articles

Transmission of soliton for a coupled Radhakrishnan–Kundu–Lakshmanan equation in an optical fiber using the Jacobi elliptical sn function method

We examine a coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) equation that includes self-phase modulation, third order dispersion, self-steepening, and cross-phase modulation effects. A propagating ultrafast pulse in nonlinear systems is described by the given equation. Utilizing the coupled Radhakrishnan–Kundu–Lakshmanan (cRKL) model, we explored the dynamics of various innovative optical solitons, such as wing-shaped, W-shaped, and brilliant solitons. We used mathematical methods like the Jacobi elliptical sn function method to get the exact analytical solution. Our results demonstrate that the self-phase modulation (SPM), self-steepening (SS), cross-phase modulation (XPM), and third order dispersion (TOD) can be effectively varied to influence the structure of the solitons. It is demonstrated that the precise balance between the self-steepening effect, the self-phase modulation, and the group velocity dispersion forms these novel W-shaped chirp-free dark solitons and dark and bright solitonic structures. By choosing appropriate settings for the physical variables, it is possible to create a graphic representation of the properties of optical solitons. The study and application of nonlinear materials with third order dispersion, cross-phase modulation, self-phase modulation effect, and self-steepening nonlinearity may take new paths as a result of our findings.

Stochastic wave solutions of fractional Radhakrishnan–Kundu–Lakshmanan equation arising in optical fibers with their sensitivity analysis

Stochastic wave solutions of fractional Radhakrishnan–Kundu–Lakshmanan equation arising in optical fibers with their sensitivity analysis

Bifurcation analysis and optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation

Bifurcation analysis and optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation

Quiescent Bright Optical Solitons for Radhakrishnan�Kundu�Lakshmanan Equation with Nonlinear Chromatic Dispersion and Power�Law of Self�Phase Modulation by Lie Symmetry

Quiescent Bright Optical Solitons for Radhakrishnan�Kundu�Lakshmanan Equation with Nonlinear Chromatic Dispersion and Power�Law of Self�Phase Modulation by Lie Symmetry

AN EFFICIENT SCHEME FOR TWO DIFFERENT TYPES OF FRACTIONAL EVOLUTION EQUATIONS

In this work, the fractional Gross–Pitaevskii equation and fractional Radhakrishnan–Kundu Lakshmanan equation are investigated. A large number of new soliton solutions are obtained by implementing a simple and effective mathematical method, which is called the fractional unified solver method. Moreover, the 3D and 2D graphs are plotted to elaborate on the dynamic characteristics of these acquired solutions.

Optical solitons of stochastic perturbed Radhakrishnan–Kundu–Lakshmanan model with Kerr law of self-phase-modulation

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.

Construction of wave solutions for stochastic Radhakrishnan-Kundu-Lakshmanan equation using modified extended direct algebraic technique

In this article, stochastic solutions of Radhakrishnan-Kundu-Lakshmanan equation (RKLE) with multiplicative noise are investigated. Studying is conducted with the aid of the modified extended direct algebraic integration technique which depended on the extended Riccati equation. To aid in our evaluation, a graphic representation of noise’s impact on the retrieved solutions is presented using MATLAB software packages.

Analysis of bifurcation and chaos in the traveling wave solution in optical fibers using the Radhakrishnan–Kundu–Lakshmanan equation

The study examines the propagation of solitary waves in optical fibers controlled by the Radhakrishnan–Kundu–Lakshmanan model (RKL) equation, which includes a cubic–quintic non-Kerr refractive index. The first step in this study involves utilizing the extended algebraic method to derive solitonic solutions for the given equation. These solutions are subsequently graphically represented for a variety of parameter values. The proposed strategy allows for the discovery of a range of solutions.The controlling model is incorporated into a planar dynamical system via the Galilean transformation, resulting in the transformation of the governing model. The effects of both the quintic nonlinearity and self-phase modulation on the perturbed and unperturbed systems are explored using the effective potential and related phase portrait. The governing model is thus transformed into a planar dynamical system. Furthermore, this study harnessed a variety of numerical techniques. These methods encompassed time series analysis, phase portraits examination, and meticulous sensitivity inspections. Additionally, we employed a Poincaré section to assess the equation’s responsiveness to external perturbations. The outcomes reveal a fascinating observation: the perturbed system’s behavior shifts from a quasi-periodic state to a chaotic one, contingent upon the amplitude and frequency of the external perturbation. Moreover, we conducted multistability analysis for specific sets of physical parameters, uncovering the equation’s tendency to exhibit multistability in such scenarios.

Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law

In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavior of the associated regular system and we obtain bifurcations of the phase portraits of the traveling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, and the peakon, homoclinic and heteroclinic solutions.

Solitons to the time-fractional Radhakrishnan–Kundu–Lakshmanan equation with $$\beta$$ and M-truncated fractional derivatives: a comparative analysis

Solitons to the time-fractional Radhakrishnan–Kundu–Lakshmanan equation with $$\beta$$ and M-truncated fractional derivatives: a comparative analysis

Soliton solutions and dynamics analysis of fractional Radhakrishnan–Kundu–Lakshmanan equation with multiplicative noise in the Stratonovich sense

The main objective of this paper is to study the soliton solutions and dynamics analysis of the fractional Radhakrishnan–Kundu–Lakshmanan equation with multiplicative noise in the Stratonovich sense. Firstly, the wave transformation is used to obtain the nonlinear ordinary differential equation, and then the nonlinear ordinary differential equation is transformed into a two-dimensional plane dynamic system with a Hamiltonian system. Secondly, the phase portrait and sensitivity of the plane dynamic system and its perturbed system are studied using Maple software. Thirdly, the soliton solutions of the stochastic fractional Radhakrishnan–Kundu–Lakshmanan equation can be constructed, and the Jacobian function solutions and hyperbolic function solutions are obtained. Finally, some three-dimensional and two-dimensional diagrams of the obtained solutions are also drawn. Moreover, the modulation stability of the equation under consideration is also given.

Diverse optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation for the light pulses

In this paper, we study the Radhakrishnan–Kundu–Lakshmanan equation (RKLE) that plays a key role in modeling the nonlinear propagation of the light pulses. Two novel methods namely Wang’s Bäcklund transformation-based method and Wang’s direct mapping method are employed to construct the diverse exact optical soliton solutions. Abundant exact solutions like the bright soliton solution, dark soliton solutions, singular soliton solutions, algebraic solitary wave solutions and the singular periodic wave solutions expressed in the form of the rational function type, double-exp function type, Sin-Cos function type, Tan function type, Cot function type, Sinh-Cosh function type, Tanh function type, Coth function type, Sech function type, Csch function type, Sec function type and Csc function type are obtained. The dynamics of the different exact solutions are presented through the 3D plot, contour and 2D curve, and the corresponding physical interpretations are elaborated in detail. It is confirmed that the proposed methods are effective and powerful, and can be adopted to construct the optical solitons of the other PDEs arising in the optical physics.

Dispersive Optical Solitons with Radhakrishnan–Kundu–Lakshmanan Equation Having Multiplicative White Noise by Enhanced Kudryashov's Method and Extended Simplest Equation

This article is about dispersive optical solitons with Radhakrishnan–Kundu–Lakshmanan equation with power-law of nonlinear refractive index in presence of multiplicative white noise by the usage of Itˆo calculus. The soliton solutions contain the Wiener process embedded into its phase component. Two integration algorithms make this retrieval possible and they are enhanced Kudryashov’s method and the extended simplest equation approach.

Dispersive optical solitons and conservation laws of Radhakrishnan–Kundu–Lakshmanan equation with dual–power law nonlinearity

The current paper implements three elegant approaches to recover a complete spectrum of optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation with dual–power law of nonlinear refractive index. The conservation laws are also recovered by the usage of multipliers approach. The parameter constraints for the existence of such solitons are also enumerated. The numerical simulations of the recovered soliton solutions are also presented.

Traveling wave solutions for the Radhakrishnan–Kundu–Lakshmanan equation with a quadrupled nonlinearity law

This study investigates the optical soliton propagation for the new version of the Radhakrishnan–Kundu–Lakshmanan equation with a quadrupled-power law structure of self-phase modulation. An improved modified extended tanh-function procedure is implemented to procure novel optical solitons and several solution types for the governing model. The obtained solitons are bright, dark, and singular, along with the rational, exponential, and Weierstrass function solutions. The retrieved solitons emerged with their constraint conditions.

Comment on “Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation in the presence of perturbation term and having Kerr law”

We analyzed a recent paper (Ozdemir, 2022). The author used three approaches to construct solutions of Radhakrishnan–Kundu–Lakshmanan equation — the generalized projective Riccati equations method, the simple version of the new extended auxiliary equation method, and unified Riccati equation expansion method. We demonstrate that the first approach used by the author is erroneous. The second approach, which is, in fact, a modification of the Kudryashov method was used in an inefficient version with unnecessary restrictions. The third approach leads to several solutions that are equivalent to one. It is shown that the solutions presented in paper are wrong. The correct solutions of the RKL equation are presented.

ANALYTICAL SOLUTIONS FOR TIME-FRACTIONAL RADHAKRISHNAN–KUNDU–LAKSHMANAN EQUATION

In this paper, two algebraic methods are applied for solving a class of conformable fractional partial differential equations (FPDEs). We use these methods for the time-fractional Radhakrishnan–Kundu–Lakshmanan equation. With these methods, further solutions can be obtained compared with other approaches and techniques. The exact particular solutions include the exponential solution, trigonometric function solution, rational solution and hyperbolic function solution. These methods are very effective to obtain exact solutions of many fractional differential equations.

Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation in the presence of perturbation term and having Kerr law

Purpose:In this research study, obtaining the analytical and soliton solutions to the perturbed Radhakrishnan–Kundu–Lakshmanan (RKL) equation with Kerr law nonlinearity is aimed via the generalized projective Riccati equations method (GPREM), a simple version of the new extended auxiliary equation method (SAEM26), and unified Riccati equation expansion method (UREEM). At the same time, the roles of some parameters included in the perturbed RKL equation on soliton dynamics are analyzed. Methodology:The presented methods are successfully employed to the perturbed RKL equation. In the application of the presented methods, to convert the perturbed RKL equation into a nonlinear ordinary differential equation, we choose suitable complex wave transformation for the proposed model. Later, a linear equation system is derived using the GPREM, SAEM26, and UREEM, the system is solved, the appropriate solution sets are obtained, and the soliton solutions are achieved, respectively. Findings:The singular, bright and dark soliton solutions are generated by choosing the suitable set and parameter values. To comprehend the physical dynamics of some solutions, 3D, contour, and 2D graphs are demonstrated. In addition, 2D graphs are drawn to show how some parameters in the main equation have an effect on soliton behaviors. The examination indicates that the model parameters have a substantial effect on the soliton dynamics. Depending on the soliton forms, the effect can be varied. The results presented in this paper will be useful for future works in soliton theory and the presented methods can be effectively implemented to such equations. Originality:The effects of the model parameters included in the perturbed RKL equation on soliton dynamics are analyzed for the first time in this study.

Optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation by two effective approaches

Optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation by two effective approaches

Optical multi-wave, M-shaped rational solution, homoclinic breather, periodic cross-kink and various rational solutions with interactions for Radhakrishnan–Kundu–Lakshmanan dynamical model

This paper retrieves different types of solutions such as [Formula: see text]-shaped rational solutions with one and two kinks, homoclinic breather, multi-waves, periodic cross-kink and kink-cross rational solutions for Radhakrishnan–Kundu–Lakshmanan equation (RKLE). We will study the [Formula: see text]-shaped interaction with rogue and kink, we will also obtain the [Formula: see text]-shaped interaction with periodic and kink, periodic cross-rational solutions. At the end, we will express the graphical representation for our newly achieved solutions.