Optical Soliton solutions for stochastic Davey-Stewartson equation under the effect of noise

In this manuscript, we investigates the stochastic Davey-Stewartson equation under the influence of noise in It o <^> \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{o}}$$\end{document} sense. This equations is a two-dimensional integrable equations, are higher-dimensional variations of the nonlinear Schr & ouml;dinger equation. Plasma physics, nonlinear optics, hydrodynamics, and other fields have made use of the solutions to the stochastic Davey-Stewartson equations. The Sardar subequation method is used that will gives us the the stochastic optical soliton solutions in the form of dark, bright, combine and periodic waves. These exact optical soliton solutions are helpful in understanding a variety of fascinating physical phenomena because of the importance of the Davey- Stewartson equations in the theory of turbulence for plasma waves or in optical fibers. Additionally, we use Mathematica tools to plot our solutions and exhibit a series of three-dimensional, two-dimensional and their corresponding contour graphs to show how the noise affects the exact solutions of the stochastic Davey-Stewartson equation. We show how the stochastic Davey-Stewartson solutions are stabilised at around zero by the multiplicative Brownian motion.