Analyzing the influence of multiplicative white noise on optical solitons in birefringent fibers through the perturbed Gerdjikov–Ivanov model

This study investigates the effects of multiplicative white noise on optical soliton perturbations with the Gerdjikov-Ivanov equation. Using novel analytical techniques, which include the enhanced direct algebraic method and the new projective Riccati equation method, we study the dynamics of soliton solutions. Our investigation uncovers a wide range of soliton solutions, encompassing bright, dark, singular, and straddled solitons. Additionally, we obtain solutions that are represented using Jacobi and Weierstrass doubly elliptic functions. These solutions can be reduced to soliton types under certain conditions. The motivation for this study arises from the crucial role that the Gerdjikov-Ivanov equation plays in a wide range of applications, highlighting its importance in the analysis of nonlinear wave propagation. The originality of our contribution lies in providing a novel structural framework for studying the Gerdjikov-Ivanov equation in birefringent fibers with multiplicative white noise, an area that has not been previously examined. The primary advantage of this study is its potential to significantly enhance our understanding and predictive capabilities regarding the dynamics of nonlinear wave propagation in complex optical media, thereby opening up new avenues for research and application in the field of photonics and optical telecommunications. The validity of our findings is supported by graphical plots that vividly depict the dynamics of certain solitons, offering insights into the impact of white noise on their behavior. This study not only enhances the theoretical comprehension of the Gerdjikov-Ivanov equation but also contributes new analytical techniques and solutions to the existing literature, thus facilitating future research on the topic.