Abstract
In this paper, we examine numerous soliton solutions of the nonlinear (3+1)-dimensional stochastic Schrödinger equation which is indispensable for describing wave propagation in noisy or random conditions, and catches the interaction between nonlinearity and stochasticity. The proposed model is applicable in various fields, namely optics, fluid dynamics, Bose-Einstein condensates, and plasma physics. It is fundamental to explain processes like phase transitions, noise-induced stability, and solitonal resilience. Incorporating nonlinear dynamics with stochastic processes provides understanding of complex systems in realistic, noisy surroundings, hence improving basic research and practical uses. To acquire the proposed results, we use advanced analytical approaches such as modified F-expansion technique, the Riccati extended modified simple equation technique, and the generalized [Formula: see text]-expansion method. The nonlinear partial differential equation is transformed into its corresponding ordinary differential equation by means of the wave transformation to investigate the required soliton solutions. The presented methods provide numerous soliton solutions: bright, dark, combined, bright-dark, and singular solitons. The results show the efficiency of the used methods in solving complicated nonlinear partial differential equations and their adaptability. We investigate the optical soliton solutions of the system under a wide range of physical parameter sets and values. We present how solutions behave for different parameter values employing a number graph structures. This study provides new insights in the fields of higher-dimensional nonlinear and nonlinear scientific wave phenomena by analyzing the efficiency of modern approaches and describing the special behaviors of a system's nonlinear dynamics.