Analysis of Brownian motion in stochastic Schrödinger wave equation using Sardar sub-equation method

Abstract

In this paper, the stochastic nonlinear Schrödinger equation (NLSE) forced by multiplicative noise that represents the temporal change of fluctuations is examined in a more extended form. Symmetry reduction (nonclassical symmetry) is used to convert the nonlinear partial differential equation into a nonlinear ordinary differential equation to obtain new optical soliton solutions. The Sardar sub-equation method is suggested to solve this stochastic nonlinear problem. The obtained stochastic solitons illustrate the dispersion of waves in optical fiber transmissions. This approach enables us to study a wide range of solutions with significant physical perspectives, including dark solitons, bright solitons, singular and periodic solitons with their noise term effects involved in Brownian motion based on the Itô sense. The noise term effects on the solitons are presented using 3D and 2D graphs. The results and calculations show the significance, accuracy and efficiency of the method. Various stable and unstable nonlinear stochastic differential equations that are found in mathematics, physics and other applied areas can be solved using this technique.