In this article, we analyze the stochastic nonlinear Kodama (SNLK) equation driven by multiplicative noise in the Stratonovich sense. Two different approaches, namely the generalized Riccati equation mapping approach and the improved \(\mathcal {F}\) -expansion method, are employed to derive novel solutions, including dark, singular, combo, periodic, periodic-singular, trigonometric, hyperbolic, and rational stochastic solutions. We illustrate the effects of multiplicative noise on the exact solutions of the SNLK equation by plotting multiple 2D and 3D graphical representations. Additionally, sensitivity analyses are conducted utilizing the Runge–Kutta method. The results are novel and have not been investigated before for this system, demonstrating the simplicity, efficacy, and dependability of these methods in the analysis of nonlinear models in plasma physics, nonlinear optics, and fluid dynamics.
