Optical solitons of the (1+1)-dimensional perturbed complex Ginzburg-Landau equation having the Kerr law in the absence of the chromatic dispersion

Abstract

This study delves into the soliton solutions of the (1+1)-dimensional perturbed complex Ginzburg-Landau equation characterized by Kerr law, under the condition of absent chromatic dispersion. The complex Ginzburg-Landau equation, a basic equation in nonlinear science, describes various complex systems including optical fibers, Bose-Einstein condensates, and fluid dynamics. By applying the Auxiliary equation scheme, we explore the bright and kink soliton solutions and modulation instability of the considered model by incorporating Kerr nonlinearity, which describes the intensity-dependent refractive index in optical media. Furthermore, detailed 3D-surface and 2D graphs of obtained soliton solutions have been added. Additionally, graphs illustrating the impacts of various parameters for the considered model on soliton solutions are presented in this study. Our findings provide deeper inspirations into the structures of soliton formation and propagation in nonlinear media, contributing to the theoretical understanding and potential implementations in optical communication systems and beyond. This work underscores the critical role of nonlinearity in forming solitons and offers a framework for further exploration of perturbed nonlinear systems devoid of chromatic dispersion effects.