Soliton dynamics related to the stochastic Gross–Pitaevskii equation in the presence of random fluctuations

The main goal of this paper is to investigate the soliton dynamics of the stochastic Gross–Pitaevskii equation (SGPE), which is forced by multiplicative white noise by using new extended direct algebraic method. The SGPE serves as a fundamental model in the study of Bose–Einstein condensates (BECs) and related systems, capturing complex nonlinear interactions in ultra-cold atomic gases. Incorporating random fluctuations into the SGPE framework reflects real-world scenarios where environmental noise plays a significant role. Utilising a direct algebraic method enables a comprehensive exploration of the interplay between deterministic soliton behaviour and stochastic perturbations. Through analytical analysis, we unveil the intricate effects of random fluctuations on soliton formation, propagation and stability. This paper not only advances our fundamental understanding of soliton dynamics in stochastic systems but also provides practical tools for harnessing and controlling soliton behaviour in complex, fluctuating environments.