Stochastic soliton dynamics in the perturbed Gerdjikov-Ivanov equation with multiplicative noise via the new Jacobi elliptic function expansion method

This study investigated the perturbed Gerdjikov-Ivanov equation (PGIE) affected by multiplicative noise in the Itô sense. The equation examined the influence of stochastic perturbations on its solitonic structures through an analytical and computational method. We found precise soliton solutions and examined their stability through the new Jacobi elliptic function expansion method. Subsequent to the mathematical study, graphical representations were executed. The results enhance the comprehensive understanding of nonlinear stochastic wave equations and their applications in optical fiber communications and many physical systems. Subsequently, the three-dimensional and two-dimensional model demonstrate the presence of bright and dark solitons, Jacobi-elliptic solutions, and periodic solutions for various values of $\sigma$.