Chirped Optical Soliton Perturbation for Fokas-Lenells Equation with Time–Dependent Coefficients and Multiplicative White Noise

This paper investigates the stochastic Fokas-Lenells Equation (FLE) with time-dependent coefficients and multiplicative white noise to model the propagation of chirped optical solitons in nonlinear dispersive media. The equation captures complex dynamics in realistic fiber systems, accounting for variable dispersion, Kerr nonlinearity, Raman effects, and stochastic perturbations arising from thermal and amplifier-induced fluctuations. Two analytical techniques, namely the extended simplest equation method and the enhanced direct algebraic method, are employed to derive exact soliton solutions. These methods offer a systematic and flexible analytic framework that efficiently handles stochastic and variable-coefficient systems, enabling closed-form solutions where conventional techniques often struggle. These include bright, dark, kink-shaped, singular, and elliptic solitons under specific parametric conditions. The richness of the obtained solution classes demonstrates the strength and versatility of the adopted approach in capturing diverse nonlinear wave profiles in noisy, inhomogeneous optical media. A key result is that the multiplicative noise affects only the soliton phase, preserving the amplitude and shape of the waveform. This demonstrates the inherent stability of soliton structures in noisy environments. The results highlight the analytical power of the proposed methods and provide deeper insights into robust pulse dynamics in realistic stochastic fiber systems, paving the way for future studies in dispersionmanaged fibers, optical lattices, and structured photonic media.