Effects of white noise on straddle and soliton dynamics in birefringent fibers using the novel Kaup-Newell equation approach

Abstract

This research delves into the intricate analysis of the Kaup-Newell equation when affected by multiplicative white noise within birefringent fibers, a topic of growing importance in modern communication systems. This study introduces a novel approach to this model, which is reported in this paper for the first time; the additional impact of the multiplicative white noise effect is also incorporated. Through applying two distinct methodologies, the enhanced direct algebraic method and the new projective Riccati equations method, this investigation illuminates the dynamic behaviors exhibited by this equation under stochastic conditions. The outcomes of this rigorous mathematical exploration encompass the identification of bright, dark, and singular soliton solutions and straddled soliton solutions. Furthermore, the research uncovers Jacobi elliptic doubly periodic solutions and Weierstrass elliptic doubly periodic function solutions. The comprehensive nature of these results advances the understanding of nonlinear wave propagation in birefringent fibers. It provides a theoretical groundwork for future experimental and practical applications in optical fiber technology. This study underscores the significance of integrating noise considerations into modeling optical fiber dynamics, which could have profound implications for developing more resilient and efficient communication systems.