Solitary Wave Structures Under Stochastic Influence in a Nonlinear Optical System Governed by an Augmented Fokas-Lenells Equation

This paper investigates the stochastic dynamics of optical solitons in the Fokas-Lenells equation, incorporating nonlinear chromatic dispersion and generalized quadratic-cubic Self-Phase Modulation (SPM). As a non-trivial extension of the Nonlinear Schrödinger Equation (NLSE), the Fokas-Lenells framework accurately models ultrashort pulse propagation in optical fibers where higher-order nonlinearities and complex dispersion effects dominate. We employ the Modified Extended Mapping Method (MEMM) to derive comprehensive analytical solutions under stochastic perturbations that realistically represent noise in fiber-optic systems. Our approach yields multiple solution classes, including dark and singular solutions, exponential-type solutions, periodic wave solutions (both trigonometric and elliptic), Jacobi elliptic function solutions, Weierstrass elliptic solutions, and hyperbolic function solutions. The MEMM proves particularly effective in handling the mathematical complexity of the stochastic NLSE class of equations, maintaining solution integrity while accommodating physical constraints. Through systematic parametric analysis, we identify critical condition regimes where each solution type emerges, providing new insights into noise-resistant soliton propagation in advanced photonic systems.