On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise

The nonlinear Schrödinger equation (NLSE) is a fundamental and significant physical model that plays a crucial role in demonstrating the dynamics of optical solitons in the theory optical fibers. The propagation of solitons in nonlinear optical fibers has garnered substantial interest due to its broad spectrum of applications, particularly in ultrafast signal routing systems and short light pulses for communications. This article focuses on investigating the impact of multiplicative noise on the solutions of this governing model. To achieve this, three distinct methods, namely the enhanced modified extended tanh expansion (METE) method, the generalized Kudryashov (GK) approach and the extended modified auxiliary equation mapping (EMAEM) method are employed to obtain a new variety of stochastic solutions. The perception of how noise intensity impacts the transmission of waves is a fundamental and critical issue in various fields. In the context of this study, an equation describes an exact wave pattern under the condition that s (representing noise intensity) equals zero. In such cases, the observed pattern remains undisturbed and matches the expected theoretical wave pattern. However, as the strength of noise s increases, the observed pattern begins to deviate from the ideal wave pattern and exhibits signs of damage or distortion. Furthermore, the stability analysis for the stochastic NLSE is performed, providing valuable insights into the behavior solutions as the strength of multiplicative noise increases. The validation of computational results through stability analysis enhances the confidence in the findings of the study. All the mathematical calculations, as well as graphical representations, have been meticulously achieved to present a comprehensive and detailed understanding of the impact of multiplicative on soliton propagation in nonlinear optical fibers.