Abundant Elliptic, Trigonometric, and Hyperbolic Stochastic Solutions for the Stochastic Wu–Zhang System in Quantum Mechanics

In this article, we look at the stochastic Wu–Zhang system (SWZS) forced by multiplicative Brownian motion in the Itô sense. The mapping method, which is an effective analytical method, is employed to investigate the exact wave solutions of the aforementioned equation. The proposed scheme provides new types of exact solutions including periodic solitons, kink solitons, singular solitons and so on, to describe the wave propagation in quantum mechanics and analyze a wide range of essential physical phenomena. In the absence of noise, we obtain some previously found solutions of SWZS. Additionally, using the MATLAB program, the impacts of the noise term on the analytical solution of the SWZS were demonstrated.