Optical solitons of the perturbed Schrödinger-Hirota equation with Kudryashov's law and spatio-temporal dispersion

Abstract

This paper employs the new Kudryashov method, noted for its ease of application to complex equations and computational efficiency, to obtain solutions for the perturbed Schr & ouml;dinger-Hirota equation with Kudryashov's law and spatio-temporal dispersion. After deriving the solutions, we perform a graphical analysis to investigate how key parameters affect soliton dynamics. Kudryashov's law provides an effective framework for modeling nonlinear terms, offering a refined description of soliton behavior and wave propagation in optical fibers. We visualize the analytical solutions using three-dimensional, contour, and two-dimensional plots, which highlight the characteristics of bright, dark, and W-shaped solitons and illustrate the effects of key parameters on their behavior. The findings offer valuable insights into optimizing next-generation optical technologies and contribute to broader fields such as nonlinear optics and photonics.