Practical Analytical Approaches to Soliton Solutions, Dynamical Properties and Chaotic Behaviors of the Stochastic Nonlinear Schrödinger Equation Under the Influence of Multiplicative White Noise

Abstract

This paper investigates the soliton solutions, dynamic properties and chaotic behaviors of the generalized derivative stochastic nonlinear Schrödinger equation with multiplicative white noise. The model has a profound impact on the nonlinear optical phenomena. Firstly, the trial equation method is employed for mathematical analysis from which the solutions are derived straightforwardly using the direct integration method without additional assumptions. Secondly, a qualitative analysis of the equation is conducted to verify the existence of some special solutions. Based on the complete discrimination system for the polynomial method, this study successfully solves fourth- and fifth-degree polynomial equations and obtains richer and more comprehensive soliton solutions. Notably, stochastic averaging is adopted, which alters the periodic characteristics of the solution to exhibit more randomized and homogenized behaviors. Thirdly, the two-dimensional and three-dimensional graphs visually demonstrate the amplitude variations caused by the delay factor resulting from white noise. Finally, chaotic behaviors provide crucial theoretical support for nonlinear wave propagation under stochastic perturbations.