Dynamics of optical solitons of the pure cubic derivative NLSE with multiplicative white noise using analytical schemes

In this article, we investigate the analytical and computational dynamics of optical solitons modulated by the pure cubic derivative nonlinear Schrödinger equation under multiplicative white noise. The model portrays the interaction among higher-order dispersion, self-phase modulation, and stochastic perturbations in birefringent optical fibers, which provides a comprehensive framework for analyzing nonlinear pulse propagation. To thoroughly examine these intricate nonlinear dynamics, we systematically implement three advanced analytical schemes, namely, the extended Kudryashov method, the unified Riccati equation expansion, and the Weierstrass-type projective Riccati equation expansion approaches. These approaches yield a rich set of exact traveling-wave solitons, including bright, dark, singular, and Weierstrass elliptic solitons. The elliptic solitons degenerate into hyperbolic, trigonometric, and periodic forms under certain parameter constraints, extending the assortment of soliton structures. Numerical simulations illustrate how white noise impacts soliton amplitude, phase stability, and propagation dynamics. Furthermore, we conduct a detailed stability analysis that reveals how variations in system parameters lead to transitions between stable centers and unstable saddle points when multiplicative white noise is present. These findings advance the theoretical understanding of stochastic soliton behavior, demonstrating the robustness and modulation of optical pulses in noisy nonlinear environments.