New stochastic traveling wave solutions for the Kundu–Mukherjee–Naskar equation with random variable coefficients

The stochastic Kundu–Mukherjee–Naskar (SKMN) equation with multiplicative noise is considered. We apply the appropriate transformation to the SKMN to create another Kundu–Mukherjee–Naskar equation with random variable coefficients. We use the mapping approach to provide innovative trigonometric, hyperbolic, and rational solutions for KMNE-RVCs. Following that, we obtain the solutions of SKMN. For the first time in the Kundu–Mukherjee–Naskar equation, we propose that the solution to the wave equation is stochastic, while all prior studies assumed it was deterministic. Some previous results are generated. Furthermore, we provide a variety of graphical representations to show how multiplicative noise affects the exact solutions of the stochastic Kundu–Mukherjee–Naskar.