Abstract

Abstract This paper explores innovative solutions for the Stochastic Schrödinger-Hirota equation within the context of birefringent fibers with cubic-quintic nonlinearity, emphasizing incorporating multiplicative white noise in the Itô sense. Leveraging the Nucci reduction method, the study focuses on obtaining exact solutions, shedding light on the intricate interplay between quantum mechanics and stochastic processes. The Nucci reduction method is a powerful tool to facilitate the derivation of precise solutions, showcasing its efficacy in unravelling complex mathematical structures and providing valuable insights into the behaviour of quantum systems under the influence of diverse parameters. In addition, two effective and convenient procedures are employed to extract bright, dark, and unique soliton solutions, as well as their combination. Exploring these solutions contributes to a deeper understanding of the equation’s dynamics, particularly in real-world applications such as quantum optics and condensed matter physics. Additionally, this study incorporates graphical depictions of specific solutions to demonstrate the effect of white noise on solitons visually.