New periodic wave solution for time-fractional perturbed nonlinear Schrödinger equation arising in optical fiber via newly extended mapping scheme

Abstract

In this study, we investigate the time-fractional perturbed nonlinear Schr & ouml;dinger equation in the context of optical fibers using the newly extended mapping scheme. As a result, many types of traveling wave solutions are obtained, including novel solitary wave solutions, triangular, hyperbolic, and periodic wave solutions expressed in terms of Jacobi elliptic functions. Solutions are obtained as well in the limiting cases for & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell$$\end{document} approach 0 or 1. By assigning specific values to the free parameters, the physical significance of the 2D and 3D geometric shapes of the derived solutions is discussed, and the corresponding physical variations are illustrated. This work demonstrates the applicability of the proposed method to a broader class of nonlinear evolution equations in physics and engineering.