Abstract
In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.
Highlights
IntroductionThe optical solitons have become an important research topic in the physical and natural sciences
The optical solitons have become an important research topic in the physical and natural sciences.It has been found that solitons play a significant role in various branches of science, such as optical fibres, plasma physics, nonlinear optics, and many other fields [1,2,3,4,5]
The present study concentrated on the conformable space–time fractional complex GL equation under the dominance of three different laws of nonlinearity
Summary
The optical solitons have become an important research topic in the physical and natural sciences. A variety of powerful mathematical approaches have been developed to derive soliton solutions for many physical models. The study of physical models with fractional derivatives has attracted a great deal of attention since some materials are well described as fractal media. To investigate such models, several definitions of fractional derivatives such as Caputo [21], Caputo–Fabrizio [22], Riemann–Liouville [23], and Grünwald–Letnikov [24] have been introduced. Contrary to the previous studies, we will consider a = 4$ instead of ν = 2$ The aim of this assumption is to present the difference between the behaviour of solitons derived here and in the previous studies
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