This study explores the optical soliton solutions of perturbed high-order nonlinear Schrödinger equation with a quintic nonlinearity. Three newly developed techniques namely, modified simplest equation, new Kudryashov’s, and generalized Arnous methods, are utilized to find several novel families of optical soliton solutions, encompassing bright, dark, singular, combined, and periodic solitons, with the help of various parameters. The solutions obtained are examined through Mathematica, which encompasses an extensive collection of mathematical functions, such as trigonometric, hyperbolic, logarithmic and rational functions. Furthermore, the obtained results are visually depicted using 3D, and 2D plots for various parametric values. This work makes a substantial advancement in comprehending the intricate and uncertain dynamics of this mathematical model. The in-depth investigation of optical soliton solutions not only enhances our comprehension of basic wave phenomena but also offers significant insights for tackling nonlinear equations across diverse scientific areas like plasma physics, optical fiber communications, and nonlinear dynamics.
Amer et al. (Fri,) studied this question.