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

The fractional perturbed nonlinear Schrödinger equation is important to model the dynamics of ultra-short pulses in lasers, solitons behavior in nonlinear optical fiber, signal processing, spectroscopy, etc. In this study, we construct assorted soliton solutions to the aforementioned equation utilizing a couple of analytical approaches, namely the (G′/G,1/G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(G^{\prime}/G,1/G)$$\end{document}-expansion method and the improved F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F$$\end{document}-expansion method, to simulate the behavior of localized wave packets known as soliton in the presence of nonlinear perturbation and fractional derivatives through closed-form solutions. The solutions comprise arbitrary parameters, and for appropriate values of these parameters, several typical solitons, including compacton, periodic, irregular-periodic soliton, bell-shaped soliton, V-shaped soliton, kink, and some others are established. We investigate the effect of the fractional-order derivatives, and the graphs confirm that the fractional derivatives affect the amplitude, velocity, and width of the solitons. This study establishes the reliability of the implemented methods for finding soliton solutions of other nonlinear evolution equations.