Optical soliton solutions of the higher-order nonlinear Schrödinger equation with Kerr law nonlinearity of self-phase modulation

The primary aim of this article is to examine the higher-order nonlinear Schrödinger equation, which describes the propagation of dispersive pulses in fiber optics, characterized by self-phase modulation and Kerr law nonlinearity, and to employ the unified Riccati equation expansion method. Our objective is not only limited to obtaining various soliton solutions using the technique proposed in the article but also to investigate the impact of higher-order dispersion terms on soliton propagation in the examined model. New and significant physical features of the investigated model, influenced by higher-order dispersion terms and Kerr law media, have been added to the literature. Furthermore, the dynamic behaviors and physical significance of some soliton solutions for appropriate values of the model parameters have been demonstrated. The obtained soliton solutions include dark and M-shaped solitons. The 3D, 2D, and contour plots of these solutions are presented to interpret the physical significance of the problem under consideration. It has been observed that the proposed approach is an effective analytical method that can be utilized to obtain optical solutions to various complex nonlinear problems.