The Effect of Standard Wiener Process on the Stochastic Davey–Stewartson Model Via the Jacobi Elliptic Function Expansion Approach

ABSTRACT In this paper, the stochastic Davey–Stewartson mathematical model of hydrodynamics, nonlinear optics, and plasma physics is considered. This model is impressive in that it can describe complex multidimensional wave processes under the action of random factors, which is typical for natural physical systems. The primary aim of this study is to acquire and examine exact stochastic solutions of the Davey–Stewartson equation via an analytical method. The problem is initially decomposed into real and imaginary parts, yielding a system of nonlinear partial differential equations (NLPDEs). The system is then reduced to a set of linear equations and associated polynomial versions. The resulting linear system gives some sets of solutions with both the model parameters and the form of the proposed solution. An appropriate set of solutions is determined, and a wave transformation is performed to allow the solutions to be obtained. The Jacobi elliptic function expansion method, a powerful analytical method, is used to get exact solutions of the Davey–Stewartson equation. This method offers a wide range of solution forms, such as singular, periodic, and trigonometric waveforms. In addition, numerical solutions are established for the study of the influence of noise on the reached solutions, and the results are presented in terms of 3D, 2D, and contour plots based on parameters obtained by an analytical procedure. The results provide new exact solutions in a stochastic environment, highlighting the importance of the process used. These findings represent novel results never previously presented in the literature.