Multiplicative brownian motion stabilizes traveling wave solutions and dynamical behavior analysis of the stochastic Davey–Stewartson equations

This article investigates the traveling wave solutions of the stochastic Davey–Stewartson equations based on the theory of the complete discriminant system of quadratic polynomials. Firstly, the stochastic Davey–Stewartson equations are transformed into the nonlinear ordinary differential equations through traveling wave transformation. By using Maple software, some two-dimensional and three-dimensional phase portraits are drawn. Secondly, according to the classification of the roots of quadratic polynomial equation, new traveling wave solutions of the stochastic Davey–Stewartson equations are obtained by using the complete discriminant system, which include rational function solutions, triangle function solutions and the Jacobi elliptic function solutions. Finally, three-dimensional-surface plots and two-dimensional-shape plots of some obtained solutions are drawn by using Maple software.