Optical solitons of space-time fractional Fokas\u2013Lenells equation with two versatile integration architectures

N Raza,Hatem R Besbes,M S Osman,Sayed Abdel-Khalek,Abdel-Haleem Abdel-Aty

doi:10.1186/s13662-020-02973-7

Abstract

Nonlinear Schrödinger’s equation and its variation structures assume a significant job in soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with a relatively new definition of local M-derivative have been recovered by utilizing improved tan (frac{phi (eta )}{2})-expansion method and generalized projective Riccati equation method. The obtained solutions are periodic, dark, bright, singular, rational, along with few forms of combo-soliton solutions. These solutions are given under constraints conditions which ensure their existence. The impact of local fractional parameter is featured by its graphical portrayal. 2D and 3D diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences. Our study shows that the suggested schemes are effective, reliable, and simple for solving different types of nonlinear differential equations.

Highlights

From the past three decades, optical solitons emerge as a fast growing area of research due to their use in transmission technology, through different forms of wave-guides
5 Results and discussion This section deals with graphical demonstration of the obtained results and provides a brief discussion on the effect of fractional parameter α
An M-fractional FL equation representing the propagation of short light pulses in the monomode optical fibers is investigated using the improved tan(

Summary

Introduction

From the past three decades, optical solitons emerge as a fast growing area of research due to their use in transmission technology, through different forms of wave-guides. Solitons are utilized to represent the particle-like properties of nonlinear pulses. The importance of solitons is due to their presence in a variety of nonlinear differential equations portraying many complex nonlinear phenomena, including acoustics, nonlinear optics, telecommunication industry, convictive fluids, plasma physics, condensed matter, and solid-state physics. Nonlinear Schrödinger’s equation and its variant forms are used in dispersive mediums in different fields of mathematical physics and have been studied mathematically in recent years [1–15]. Solitons exist due to an accurate balance among nonlinearity and group velocity dispersion (GVD) in the area. If the value of GVD is small, this balance may be at risk. To keep the balance among the two, expression terms with dispersive effects need to be in-

Objectives

Results

Conclusion