Identification of stochastic optical solitons in a generalized NLSE characterized by fourth order dispersion and weak nonlocality

Abstract

In this work, we investigate the stochastic traveling wave solutions for the generalized nonlinear Schr & ouml;dinger equation under the influence of the Wiener process. It encompasses weak nonlocality related parameters and higher order dispersion with higher order nonlinearity. In order to solve this problem, the improved modified extended tanh function approach is used in conjunction with an appropriate traveling wave transformation to produce new, various, and effective soliton solutions for the proposed model using the computational tool Wolfram Mathematica. We used MATLAB packages to create both 2D and 3D visual representations of the equation in order to better understand its physical meaning. The graphical representations provide useful insights into several aspects of the dynamics of the problem. Our range of solutions includes dark, bright, singular solitons, Jacobi elliptic functions, exponential, periodic, and singular periodic solutions, all of which may be obtained by varying the values of our parameters. This paper represents the first time insertion of stochastic influences into a specified nonlinear wave equation, including impact analysis. Our computer study validates the efficacy and adaptability of our approach in solving a broad range of nonlinear phenomena in the field of mathematical science and many other fields.