The analysis of traveling wave solutions and dynamical behavior for the stochastic coupled Maccari's system via Brownian motion

The stochastic coupled Maccari's system (MS) is a kind of important nonlinear partial differential equations to describe fluid flow, plasma physics, nonlinear optics and so on. In this article, the dynamical behavior and some new exact traveling wave solutions of the system are investigated. By means of complex traveling wave transformation, the system is transformed into a nonlinear ordinary differential equation. The dynamical behavior of the system as well as its perturbation case are illustrated by bifurcation theory. And then, some new stochastic traveling wave solutions of the system are extracted based on the theory of polynomial complete discrimination system. To show the effect of stochastic factor on the solutions, their structures under different Brownian motion amplitudes are compared by several sets of graphs. The results obtained in this paper have supplemented the study of the system, and the technique used to exploit the traveling wave solutions are effective.