The new stochastic solutions for three models of non-linear Schrödinger’s equations in optical fiber communications via Itô sense

Abstract

In this paper, we consider three models of non-linear Schrödinger’s equations (NLSEs) via It\^{o} sense. Specifically, we study these equations forced by multiplicative noise via the Brownian motion process. There are numerous approaches for converting non-linear partial differential equations (NPDEs) into ordinary differential equations (ODEs) to extract wave solutions. The majority of these methods are a type of symmetry reduction known as non-classical symmetry. We apply the unified technique based on symmetry reduction to produce some new optical soliton solutions for the proposed equations. The obtained stochastic solutions depict the propagation of waves in optical fiber communications. The theoretical analysis and proposed results clarify that the presented technique is sturdy, appropriate, and efficacious. Some graphs of selected solutions are also depicted with the help of the MATLAB packet program. Indeed, the structure, bandwidth, amplitude, and phase shift are controlled by the influences of physical parameters in the presence of noise term via It\^{o} sense. Our results show that the proposed technique is better suited for solving many other complex models arising in real-life problems.