The primary objective of this paper is to explore solitary wave solutions within the context of the stochastic Reaction–Diffusion equation, a problem that has not been previously investigated with respect to multiplicative noise. This marks a novel aspect of the current study. To accomplish this goal, we utilize two distinct integration methods: the extended Kudryashov’s method and the  G G  - expansion method. These methods are chosen for their efficacy in handling nonlinear differential equations and are applied in tandem to uncover newtrigonometric and hyperbolic stochastic exact solutions. The employment of thesemethods is crucial in generating solutions that have not been previously identified in this particular context. Subsequently