Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

Abstract

This article introduces an examination of optical soliton solutions for the perturbed fourthorder
nonlinear Schr¨odinger-Hirota equation, which plays a crucial role in optics. For the first
time, it utilizes a novel approach by applying the extended auxiliary equation method. This
equation models the propagation of optical pulses through nonlinear media, such as optical
fibers, and has been the subject of many studies. Our goal extends beyond merely acquiring
a significant number of soliton solutions using the method described in this article; we also
aim to investigate the impact of the coefficients of group velocity dispersion, parabolic law,
and fourth-order dispersion terms on soliton propagation in the problem examined. The 2D,
3D, and contour plots of the acquired dark and bright solitons, which represent the most
fundamental soliton types, are presented. Additionally, all other calculations are performed
using symbolic algebraic software. The results provide us with valuable insights, confirming
that the introduced model can be analyzed from a physical perspective. It is demonstrated
that the proposed technique is not only important but also efficient in analyzing various
nonlinear scientific problems.