Novel solitary wave solutions in a generalized derivative nonlinear Schrödinger equation with multiplicative white noise effects

This study presents a novel mathematical model grounded in the generalized derivative nonlinear Schrödinger equation, enhanced by including perturbation terms such as white noise. Our primary objective is to investigate optical solitons within this model’s framework, employing two powerful mathematical techniques: the auxiliary equation method and the generalized Riccati equation mapping method. Through these methods, we uncover diverse solutions, including solitary wave solutions, singular soliton solutions, and dark and bright soliton configurations. Significantly, this work introduces a pioneering model that marks a major advancement in the study of nonlinear optical phenomena and sheds light on the diverse solutions for optical solitons influenced by multiplicative white noise. This enriches our theoretical understanding and paves the way for further research and practical applications. The model’s integration of multiplicative white noise effects into the analysis of optical solitons signifies an innovative approach, establishing a new direction in studying nonlinear optical phenomena. Motivated by the profound implications of the nonlinear Schrödinger equation across a broad spectrum of scientific fields and the critical impact of multiplicative white noise, this study also includes meticulously crafted three- and two-dimensional plots to visually demonstrate the white noise’s influence on the obtained solitons. Overall, our findings expand the theoretical physics horizon and lay a solid foundation for future experimental validations and applications, representing a significant contribution to the field.