Revealing the optical soliton solution of the fourth-order perturbed Schrödinger-Hirota equation using Kudryashov's law

Abstract

This manuscript focusses on the fourth-order perturbed Schr & ouml;dinger-Hirota equation (SHE), which exhibits Kudryashov's law. Incorporating higher-order dispersion and nonlinearities through the inclusion of Kudryashov's law, the fourth-order perturbed Schr & ouml;dinger-Hirota equation offers a more accurate model for wave propagation in systems like optical fibres and quantum theory. Utilising the F-expansion scheme, we reveal the analytical solutions for the presented equation. Additionally, a comprehensive examination of modulation instability is performed to assess the stability properties of these solutions, identifying specific parameter ranges where instabilities occur. Moreover, detailed 3D, contour and 2D graphical visualisations illustrate some of the derived solutions. As a result, we retrieve dark, bright and periodic soliton solutions. The combination of a higher-order nonlinear model, the inclusion of Kudryashov's law and the derivation of multiple types of solitons presents a novel approach that advances the understanding of soliton behaviour in more complex systems. Additionally, the 2D graphical representations take into account the impact of certain parameters. The results provide substantial support for the theoretical understanding of complex nonlinear systems and offer practical insights for experimental design and analysis in nonlinear optics and related fields.