Propagation of Stochastic Wave Structures of the Kaup–Newell Optical Fiber Equation With Multiplicative Noise Excitation

ABSTRACT This paper investigates a comprehensive analytical and numerical examination of the stochastic Kaup–Newell equation, including multiplicative white‐noise perturbations, which serves as a prominent model for nonlinear pulse propagation in birefringent optical fibers. By applying the modified Sardar Sub equation method in conjunction with the Kumar–Malik technique, a broad class of exact traveling‐wave solutions is obtained, including elliptic, dark, bright, singular, exponential, combo, and rational wave profiles. The influence of stochastic forcing on the stability and qualitative structure of these wave patterns is studied in detail. The obtained stochastic wave structures reveal how multiplicative noise modifies nonlinear pulse evolution and wave stability, providing a deeper understanding of realistic optical fiber dynamics. Moreover, the ability of the modified Sardar Sub‐equation and Kumar–Malik methods to generate a wide spectrum of exact stochastic solutions confirms their effectiveness for the analytical investigation of nonlinear stochastic optical systems. Additionally, a sensitivity analysis is performed using the classical fourth‐order Runge–Kutta scheme to demonstrate the effects of parameter variations and initial conditions on the system dynamics. The determined results emphasize the crucial role of noise‐induced modulation in shaping nonlinear pulse evolution and polarization dynamics in birefringent fibers. The significance of this work lies in suggesting deeper insight into the interplay between randomness and nonlinearity, providing valuable guidance for the design of robust high‐speed optical communication systems and advanced photonic devices.