The impact of the Wiener process on solutions of the potential Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid

We study the $(3+1)$-dimensional stochastic potential Yu–Toda–Sasa–Fukuyama equation (SPYTSFE) forced in the Itô sense by a multiplicative Wiener process. To obtain trigonometric, hyperbolic, and rational SPYTSFE solutions, we use the Riccati–Bernoulli sub-ODE and He's semiinverse methods. The SPYTSFE may explain many exciting physical phenomena because it relates to nonlinear waves and solitons in dispersive media, plasma physics, and fluid dynamics. We show how the Wiener process affects the exact SPYTSFE solutions by introducing several 2D and 3D graphs.