Cubic-Quartic Solitons for Gerdjikov-Ivanov Equation with Differential Group Delay in Presence of Multiplicative White Noise

Abstract

This study conducts an in-depth analysis of the Gerdjikov-Ivanov equation under the influence of multiplicative white noise, specifically within the context of birefringent fibers. By employing two advanced techniques-the enhanced direct algebraic method and the innovative projective Riccati equations method-the research uncovers a range of soliton behaviors. The results identify various soliton types, including bright, dark, singular, and straddled solitons. Additionally, the study presents solutions involving Jacobi and Weierstrass doubly periodic functions, which under certain conditions, transition into soliton solutions. This research introduces a novel model, with all solutions representing original contributions to the field. The influence of white noise on these soliton structures is vividly depicted through 3D, 2D, and contour plots, providing visual insights into the dynamics of solitons in the presence of noise disturbances. These graphical representations offer a deeper understanding of soliton behavior within birefringent fibers, thereby advancing the discourse on nonlinear dynamics in optical fibers.