Unveiling complex stochastic solitons in high-dimensional nonlinear Schrödinger media with multiplicative noise and higher-order nonlinearities

Abstract Background Stochastic nonlinear Schrödinger-type models play a crucial role in describing wave propagation in complex physical systems influenced by randomness, including optical fibers, plasma environments, and fluid media. Understanding how stochastic perturbations affect soliton dynamics is essential for predicting stability, coherence, and energy transport in such systems. Method The present study investigates stochastic soliton behavior governed by the (2+1)-dimensional nonlinear Schrödinger equation (NLSE). To derive analytical stochastic wave solutions, the modified extended mapping (MEM) method is employed as an effective and flexible framework for solving nonlinear stochastic partial differential equations. The influence of stochastic perturbations is further analyzed through detailed graphical simulations for varying noise intensities. Results The MEM method yields a rich family of exact stochastic solutions, including bright solitons, dark solitons, singular soliton structures, singular periodic waves, and solutions represented through Jacobi and Weierstrass elliptic functions. Graphical analyses reveal how different stochastic perturbation levels significantly modify wave profiles, influencing amplitude, localization, and stability. Increased noise intensity is shown to deform soliton structures and affect their propagation characteristics. Conclusions The findings demonstrate the robustness, efficiency, and adaptability of the modified extended mapping method for analyzing stochastic nonlinear wave models. The results also highlight the crucial role of stochastic effects in shaping soliton morphology and stability in higher-dimensional NLSE systems, offering valuable insights for applications in optical communication, nonlinear physics, and stochastic dynamical systems.