Dynamical Characteristics and Exact Solutions of Generalized Stochastic Nonlinear Schrödinger Equation

This study presents a combined analytical and dynamical investigation of the stochastic generalized nonlinear Schrödinger equation incorporating Kerr nonlinearity, higher‐order dispersion, and multiplicative stochastic perturbations. Using the modified Kudryashov method, explicit traveling‐wave solutions corresponding to bright, dark, singular, and composite soliton structures are derived. The dynamical behavior of the reduced system is investigated through phase portraits, Poincaré sections, sensitivity analysis, stroboscopic bifurcation diagrams, and largest Lyapunov exponents. The results reveal transitions among periodic, quasiperiodic, and chaotic regimes as the external forcing parameters are varied. In the stochastic solutions, the Wiener‐process contribution enters through the phase, producing random phase modulation while preserving the deterministic amplitude envelope. Additional visualizations of the real part and stochastic phase show that, within the considered parameter family, increasing the magnitude of the stochastic parameter enhances phase fluctuations and wavefront distortions. These findings demonstrate the combined influence of nonlinear, dispersive, forcing, and stochastic effects on the dynamics of the SGNLSE and provide a unified framework for exact soliton solutions and dynamical characterization in nonlinear optical media.