The travelling wave solutions to stochastic resonant nonlinear Schrödinger equation with both spatio-temporal and inter-modal dispersions having multiplicative white noise

Abstract

This paper constructs the travelling wave solutions of the stochastic resonant nonlinear Schrödinger equation that contains the stochastic term with multiplicative white noise based on the complete discriminant system for the polynomial method. By systematically investigating the polynomial law, we derive more abundant forms of travelling wave solutions. Notably, our new insight reveals that the non-averaged state of the solutions enables the characteristics of solitons and periodic modes to be maintained. In contrast, stochastic averaging will lead to changes in the periodic and soliton characteristics. In addition, we present the model diagrams for several specific parameters, which endows physical interpretations to the spatiotemporal structure in the white noise environment.