Chirped and chirp-free optical soliton solutions for stochastic long-short wave resonant equations with multiplicative white noise

Abstract

This article introduces a novel governing model characterized by stochastic long-short wave resonant equations with multiplicative white noise applicable in fields such as telecommunications and climate modeling. The study aims to explore chirped and chirp-free soliton solutions within this framework. Using Jacobi's elliptic function method as our primary methodology, we have successfully derived various soliton solutions, including solitary waves, singular solitons, and dark and bright soliton forms which can be relevant in optical communication and nonlinear optics. Significantly, our analysis has facilitated the extraction of both chirped and chirp-free solutions applicable to the model, marking a notable advancement in soliton research. Introducing this governing model is a pioneering endeavor in the field, distinguished by its ability to model the resonance interaction between long and short waves under the influence of multiplicative white noise. This aspect holds profound implications for the understanding and application of wave dynamics in stochastic environments such as in meteorology and fluid dynamics. To underscore our findings, the manuscript includes 3D and 2D graphical representations, effectively illustrating the impact of white noise on the wave profiles of the derived solitons. Our study broadens the theoretical landscape of soliton solutions and presents a significant step forward in practically examining wave resonance phenomena under stochastic conditions.