Characteristics of stochastic solutions to the long–short-wave interaction model through Brownian process

This article aims to offer stochastic solutions for the nonlinear long-short wave interaction system (NLSWIS) via It^o sense. Using He's semi-inverse approach, some innovative travelling wave solutions are produced. These solutions are obtained using the Ritz technique. We produce the potential model that corresponds to the NLSWIS model's energy equation. We also explain how multiplicative noise affects the solutions. A few graphs are also displayed using the Matlab packet software. The developed solutions can be applied in space plasma, ocean waves, regenerating infectious for people crowds, and economic viability as a consequence of infectious these issues being controlled. In fact, the He's semi-inverse approach exhibits promise for resolving a range of nonlinear systems that arise in the applied sciences.