Exact wave structures with stochastic effects in birefringent optical fibers modeled by cubic-quintic-septic nonlinear Schrödinger equation

Stochastic optical solitons are a fascinating phenomenon in nonlinear optics where soliton-like behavior emerges in systems affected by stochastic noise. This study establishes a fundamental framework for stochastic wave propagation in birefringent fibers through the cubic-quintic-septic nonlinear Schrödinger equation (NLSE). Our modified extended mapping technique yields exact analytical solutions (bright, dark, and singular solitons, periodic structures, and Weierstrass elliptic waves) that explicitly incorporate multiplicative noise and birefringent coupling. We explore the influence of noise intensity on soliton stability and morphology through parameter analysis and visual simulations, revealing how stochastic fluctuations modify amplitude, phase, and localization. The visualized results in Figures 1-3 not only validate the analytical expressions but also provide intuitive insight into the role of noise in shaping wave evolution. These findings are crucial for the development of noise-tolerant optical soliton systems, especially in ultra-fast communication platforms, nonlinear fiber lasers, and integrated photonic circuits.