In this paper, we look at novel stochastic solutions for the coupled Maccari system through the Wiener process. The incorporation of random perturbations provides a rigorous framework for modeling physically relevant phenomena in which noise-induced effects play a significant role. Such effects naturally arise in a wide range of applications, including signal propagation in optical fibers, plasma dynamics, and the evolution of fluid interfaces, where stochastic fluctuations can substantially influence the system behavior. To generate explicit analytical solitary wave solutions, we use the extended tanh function method (ETFM), which allows for the systematic derivation of accurate stochastic wave structures, such as soliton-like, blow up, periodic, and rational-type solutions under stochastic influence. To illustrate the propagation behavior of solitary waves in the stochastic Maccari model, 2D graphical representations of selected solutions were generated using MATLAB software. The obtained solutions demonstrate complex interactions between deterministic nonlinear dynamics and stochastic fluctuations, shedding light on the modulation and stability of wave propagation in noisy environments. These discoveries not only contribute to a better theoretical understanding of stochastic nonlinear systems, but they also have potential applications in sectors where random disturbances have a large impact on wave evolution.

Magnetogasdynamics (MGD) is an interdisciplinary area of study that investigates the properties and behavior of electrically conductive gases, including plasmas and ionized fluids, when subjected to magnetic and electric fields. MGD is essential for simulating how electromagnetic fields affect electrically conducting gases, especially in flow regimes with high temperatures and speeds. This article examines a one-dimensional non-ideal isentropic magnetogasdynamic. We offer a modified version of finite volume (MVFV) method for the numerical analysis of this model. This approach represents an improved iteration of the Rusanov scheme, a widely utilized finite volume method for the numerical resolution of hyperbolic systems of conservation laws, particularly in the fields of MGD and fluid dynamics. The MVFV method is structured into two distinct phases: the predictor phase and the corrector phase. The predictor relies on the control parameter, which is responsible for the numerical diffusion of this method. The second phase reinstates the balance conservation equation. The MVFV technique's results are compared to the exact solution and the Harten–Lax–van Leer (HLL) approach in the numerical simulation. The findings validate the reliability of MGD models in effectively representing critical nonlinear phenomena and establish a foundation for forthcoming numerical simulations and experimental verification.