Exploration of Different Soliton Solutions for the Stochastic Davey– Stewartson Model Under the Influence of Noise

Abstract

In this paper, we research the stochastic Davey–Stewartson (SDS) mathematical model, which is crucial in modeling a broad variety of physical processes such as surface and internal wave propagation in hydrodynamics, transmission of light in nonlinear optical materials, and wave dynamics in plasma media. The SDS system represents an extension of the standard Davey–Stewartson equations by introducing stochastic perturbations to discuss the dynamics of waves subjected to random influences. In order to analyze this model, we begin by decomposing the governing complex-valued equation into real and imaginary parts, obtaining a coupled system of nonlinear partial differential equations. The separation enables us to build an associated linear system whose solutions are polynomials parameterized with the physical constants of the model. Using a wave transformation and choosing suitable ansatz functions, we derive a class of exact stochastic optical soliton solutions by the Kumar-Malik method, which is a robust analytical approach well known for its competence in handling nonlinear structures. We give our solutions in various functional forms like trigonometric, hyperbolic, exponential, and Jacobi elliptic functions, and thus show the generality of the method. Furthermore, we provide a classification of these solutions into distinct categories such as bright solitons, dark solitons, singular and periodic structures, and noisemodulated waveforms. For the bright soliton solutions, we study the stability and dynamical behavior by conducting numerical simulations for different intensities of noise. The graphical representation of solutions in 3D, contour, and 2D plots contains rich dynamic features like amplitude modulation, deformation of wave profiles, and stochastic bifurcation onset. A comparative study with the existing literature is provided that emphasizes the novelty of the solutions presented and the universal utility of the stochastic DS framework to model real-world nonlinear systems. This work not only provides new exact solutions but also provides a deeper understanding of the effect of randomness on the propagation of solitons, making it a significant contribution to the analytic and physical knowledge of Stochastic partial differential equations in multidimensional models of waves.