In this study, we investigate optical soliton dynamics for the coupled system of nonlinear stochastic Kaup–Newell equations incorporating multiplicative white noise following the Itô calculus. This coupled system of equations captures key solitons wave structures in birefringent fibers under stochastic environments. Firstly, we construct exact solutions in the form of stochastic solitons using the Jacobi elliptic function expansion approach (JEFEA) and the \(\left( \frac{f}{\mu f+g} \right) \) -expansion method. These methods yield various traveling and solitary wave solutions whose structures include solitonic, trigonometric, hyperbolic, and Jacobi elliptic wave forms. Several constraint conditions ensure the validity of the derived solutions. To analyze the physical structure and dynamical evolution of some selected solutions in both deterministic and stochastic regimes, graphical illustrations are presented via 2D, 3D and contour plots using Mathematica. The influence of stochastic perturbations on the soliton shape, amplitude, and stability is systematically explored. The accuracy of the obtained solutions are verified, confirming the reliability of the employed methods. Overall, this study demonstrates that these techniques offer efficient and systematic tools for solving nonlinear stochastic partial differential equations as the findings contribute novel analytical solutions to the literature and highlight the practical relevance of stochastic modeling in nonlinear optics and related fields.
