Comprehensive study of stochastic soliton solutions in nonlinear models with application to the Davey Stewartson equations.

This article investigates the stochastic Davey-Stewartson equations influenced by multiplicative noise within the framework of the Itô calculus. These equations are of significant importance because they extend the nonlinear Schrödinger equation into higher dimensions, serving as fundamental models for nonlinear phenomena in plasma physics, nonlinear optics, and hydrodynamics. This paper is motivated by the need to understand how random fluctuations affect soliton behavior in nonlinear systems. This is particularly relevant in applications such as turbulent plasma waves and optical fibers, where noise can significantly impact wave propagation. We employ the modified extended direct algebraic method for finding exact stochastic soliton solutions to the stochastic Davey-Stewartson equations. The study derives a class of exact stochastic soliton solutions, including dark, singular, rational, and periodic waves. MATLAB is used to provide visual representations of these stochastic soliton solutions through 3D surface plots, contour plots, and line plots. These solutions offer essential insights into how random disturbances influence nonlinear wave systems, particularly in turbulent plasma waves and optical fibers. To the best of our knowledge, the application of the modified extended direct algebraic method to the stochastic Davey-Stewartson equations with multiplicative noise, along with the subsequent analysis of the stabilizing effects on dark, singular, rational, and periodic stochastic soliton solutions is novel. The study demonstrates how multiplicative Brownian motion regulates these wave structures, providing new information on the impact of noise on higher-dimensional nonlinear systems.