Non-ansatz exact solutions and noise-induced chaotic dynamics in a generalized anti-cubic nonlinear stochastic system

This paper addresses the problem of stochastic propagation of light in complex nonlinear optical media by solving the generalized anti-cubic nonlinear stochastic Schrödinger equation with multiplicative white noise. Using the polynomial complete discriminant system method, it systematically reveals nine categories of exact solutions for the first time, encompassing rich forms such as soliton solutions, periodic solutions, and elliptic function solutions. Dynamical analysis reveals that the non-averaged form of the solution perfectly preserves typical soliton profiles (e.g. bell-shaped pulses, kink structures), whereas the stochastic averaging process leads to significant degradation of the soliton shape due to the intervention of the delay factor. The Lyapunov exponent uncovers perturbation-induced chaos, specifically that chaotic behaviour arises when the Lyapunov exponent is positive. This study overcomes the limitations of traditional ansatz methods, elucidates the ‘noise-soliton-chaos’ mechanism, and fosters the interdisciplinary integration of nonlinear dynamics and optical engineering.