Analyzing the diversity of wave profiles to the stochastic Davey-Stewartson equation: Application in the hydrodynamics engineering

This study investigates the stochastic Davey-Stewartson system with multiplicative noise, an important high-order nonlinear partial differential equation, within Ito calculus framework. These equations are fundamental for describing nonlinear events in domains including oceanic waves, and fluid dynamics. We use sophisticated analytical methodologies such as the modified generalised Riccati equation mapping method, the Riccati extended modified simple equation technique, and the modified F-expansion technique. Various wave profiles in the form of solitons are generated. The results demonstrate the effectiveness and versatility of the approaches for solving complex nonlinear partial differential equations. Using various graph structures, we have showed the behaviour of the solutions for different parameters values. This study contributes new insights into the field of high-dimensional nonlinearities and wave phenomena in nonlinear science by showing how multiplicative Brownian motion regulates these wave structures, providing new insights into the effects of noise on high-dimensional nonlinear systems.