New optical soliton solutions of fractional perturbed nonlinear Schrödinger equation in nanofibers

Abstract

In this article, the space-time fractional perturbed nonlinear Schrödinger equation (NLSE) in nanofibers is studied using the improved [Formula: see text] 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.

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

“…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].…”

On the exact solutions of optical perturbed fractional Schrödinger equation

“…The article (see, [30]) uses the modified Khater method for the solution of nonlinear Schrodinger perturbed problems and finds solutions in several different forms In optical fiber materials, article [31] uses the new sub-equation method and obtains many hyperbolic, trigonometric, and rational function exact solutions of the nonlinear perturbed Schrödinger equation with Kerr law nonlinearity. The space-time fractional perturbed nonlinear SchrÃdinger equation in nanofibers is investigated using the improved tan(f(ò)/2) extension method to obtain new exact solutions [32]. New closed-form soliton wave structures of solutions of Kerr's law nonlinear fractional perturbed SchrÃdinger equation are found using the tanh-coth method [33].…”

An efficient wavelet‐based approximation method for solving nonlinear fractional‐time long wave equations: An operational matrix approach

“…Das and Saha Ray [42] established a novel optical soliton solution for time-fractional resonant nonlinear Schrödinger equation in optical fiber. The same authors [43] applied a new optical soliton solution of fractional perturbed nonlinear Schrödinger equation in nanofibers. This paper discusses the numerical solution of the following fractional-time nonlinear partial differential equations:…”