Dispersive optical soliton wave solutions for the time-fractional perturbed nonlinear Schrödinger equation with truncated M-fractional conformable derivative in the nonlinear optical fibers

Das, Nilkanta; Ray, S. Saha

doi:10.1007/s11082-022-03899-y

Cited by 19 publications

(4 citation statements)

References 27 publications

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“…In recent years, derivatives of any order have been extensively used as a potent mathematical tool for modelling challenging issues. In reality their non-local feature and higher degree of freedom than ordinary derivatives have been two key factors in capturing scholars' interest in them [1][2][3][4]. One significant class of classical fractional derivatives that has attracted a lot of attention is the caputo derivative.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Analytical Approaches to Investigate Nonlinear Two-Dimensional Time-Fractional Rosenau-Hyman Equations within the Yang Transform

Ganie,

Mallik,

Khan

et al. 2024

Preprint

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The goal of the current study is to analyse several nonlinear two-dimensional time-fractional Rosenau Hymanequations. The two-dimensional fractional Rosenau-Hyman equation has extensive use in engineering and applied sciences. The fractional view analysis of two-dimensional time-fractional Rosenau-Hyman equations is discussed using the homotopy perturbation approach, adomian decomposition method, and Yang transformation. Some examples involving two-dimensional time-fractional Rosenau-Hyman equations are provided in order to better understand the suggested approaches. The solutions appear as infinite series. We offer a comparison between the accurate solutions and those that are generated employing the proposed approaches in order to demonstrate the effectiveness and applicability of the proposed techniques. The results are graphically illustrated using 2D and 3D graphs. It has been noted that the obtained results and the targeted problems real solutions are quite similar. Calculated solutions at various fractional levels describe some of the problems useful dynamics. Other fractional problems that arise in other fields of science and engineering can be solved using a modified version of the current techniques.

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Section: Introductionmentioning

confidence: 99%

An Efficient Analytical Approaches to Investigate Nonlinear Two-Dimensional Time-Fractional Rosenau-Hyman Equations within the Yang Transform

Ganie,

Mallik,

Khan

et al. 2024

Preprint

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“…plasma physics [2], telecommunications [3] and nonlinear dynamics has been a relatively active field of study in the last few decades [4]. The nonlinear Schrödinger equation (NLSE) is one of the most prominent dynamical models used to study pulse propagation in Kerr media [5].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and soliton solutions of the (1+1)-dimensional nonlinear chiral Schrödinger equation in nuclear physics

Badshah,

Tariq,

Bekir

et al. 2024

Commun. Theor. Phys.

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One of the most influential physical models for explaining the transmission of an optical soliton in optical fibre theory is the nonlinear Schrödinger equation (NLSE). Due to its many potential uses in communications and ultrafast signal routing systems, chiral soliton propagation in nuclear physics is a subject that holds a great deal of interest. This work employs a number of in-depth analytical techniques to deal with the (1+1)-dimensional chiral NLSE that describes the soliton behaviour in transmission of data and has application in the fields of nuclear physics, optics, ionised science, particle physics, and in other applied disciplines mathematical sciences. With the help of applied strategies, we are able to develop different types of solutions that demonstrate behaviour of singular soliton solution, periodic soliton solution, v-shaped soliton, chiral soliton and bell shaped soliton solutions behaviour. Additionally, we discuss the stability analysis for the established solution of the governing model to validate the scientific computations. For the best understanding of solutions behaviour the 3D, contour, and 2D graphics are included. The strategies used are reliable, simple, and efficient. The obtained solution has applications in various computational physics phenomena as well as in other real-world situations and a wide range of academic disciplines.

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“…Different types of phenomenon occurring chemically, biologically and economically, among others, are represented as non-linear partial differential equations (NLPDEs). Many different methods have been developed to gain the analytical wave solutions of these NLPDEs, i.e., the optical soliton solutions of coupled nonlinear Schrödinger equations have been gained with the use of the Kudryashov R function technique [13], some new kinds of optical soliton solutions of time-fractional perturbed nonlinear Schrödinger equations have been achieved by using the generalized Kudryashov scheme [14], by applying the modified auxiliary equation technique, optical wave solutions of time-fractional resonant non-linear Schrödinger equations have been obtained [15] and new optical wave solutions for time-fractional perturbed non-linear Schrödinger equations have been achieved by utilizing the improved tan(φ(ζ/2))-expansion scheme [16].…”

Section: Introductionmentioning

confidence: 99%

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

Alsharidi

Bekir

2023

Symmetry

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In this paper, we succeed at discovering the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering, where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of a concerned model. Finally, this technique is simple, fruitful and reliable to handle nonlinear fractional partial differential equations (NLFPDEs).

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Dispersive optical soliton wave solutions for the time-fractional perturbed nonlinear Schrödinger equation with truncated M-fractional conformable derivative in the nonlinear optical fibers

Cited by 19 publications

References 27 publications

An Efficient Analytical Approaches to Investigate Nonlinear Two-Dimensional Time-Fractional Rosenau-Hyman Equations within the Yang Transform

An Efficient Analytical Approaches to Investigate Nonlinear Two-Dimensional Time-Fractional Rosenau-Hyman Equations within the Yang Transform

Stability analysis and soliton solutions of the (1+1)-dimensional nonlinear chiral Schrödinger equation in nuclear physics

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

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