Noise-driven wave structures in the stochastic Davey–Stewartson equation

This paper investigates the stochastic Davey-Stewartson equation, which represents the evolution of weakly nonlinear wave packets under the effect of randomness. This equation is developed within a stochastic framework that incorporates multiplicative Brownian motion perturbations to reflect the impact of environmental fluctuations and noise-induced phenomena present in genuine physical systems. We apply the Riccati–Bernoulli sub-ordinary differential equation method, a unified and systematic approach that converts the stochastic Davey-Stewartson equation into solvable deterministic sub-ordinary differential equation, to obtain accurate stochastic solutions. The proposed method enables the production of a wide range of innovative stochastic wave solutions, such as solitons, breather-type structures, rational solutions, and periodic wave patterns, all characterised in terms of hyperbolic, trigonometric, or rational functions. The resulting solutions reveal intricate dynamical characteristics and demonstrate how random perturbations influence phase modulation, and stability features. The scientific significance of the resulting stochastic solutions is thoroughly examined, with a focus on applications in nonlinear optics, plasma physics, fluid dynamics, Bose-Einstein condensates, and ocean wave propagation, where random disturbances play an important role. Finally, the proposed technique is a robust and adaptable analytical tool for analysing stochastic nonlinear evolution equations, providing novel insights into noise-driven wave events in complex media.