Exact Solutions of the (2+1)-Dimensional Stochastic Chiral Nonlinear Schrödinger Equation

Sahar Albosaily,Mohammed A Aiyashi,Mahmoud A E Abdelrahman,Wael W Mohammed

doi:10.3390/sym12111874

Sahar Albosaily, Mohammed A Aiyashi + Show 2 more

Open Access

https://doi.org/10.3390/sym12111874

Copy DOI

Journal: Symmetry	Publication Date: Nov 14, 2020
Citations: 59	License type: CC BY 4.0

Affiliation: Mansoura University, Taibah University, University of Ha'il

Abstract

In this article, we take into account the (2+1)-dimensional stochastic Chiral nonlinear Schrödinger equation (2D-SCNLSE) in the Itô sense by multiplicative noise. We acquired trigonometric, rational and hyperbolic stochastic exact solutions, using three vital methods, namely Riccati–Bernoulli sub-ODE, He’s variational and sine–cosine methods. These solutions may be applicable in various applications in applied science. The proposed methods are direct, efficient and powerful. Moreover, we investigate the effect of multiplicative noise on the solution for 2D-SCNLSE by introducing some graphs to illustrate the behavior of the obtained solutions.

Highlights

Mathematical models of different phenomena in various areas of the physical sciences, including nonlinear optics, biology, economy, fluid mechanics and plasma physics, can be interpreted by nonlinear systems of nonlinear partial differential equations (NPDEs) [1,2,3,4,5,6,7,8,9]
Our study shows that the proposed three methods are reliable in handling NPDEs to establish a variety of exact solutions
The powerful Riccati–Bernoulli sub-ODE, He’s variational principle and sine-cosine methods are utilized in searching the presence of soliton solutions in quantum hall effect via the (2 + 1)-dimensional stochastic Chiral nonlinear Schrödinger equation

Summary

Introduction

Mathematical models of different phenomena in various areas of the physical sciences, including nonlinear optics, biology, economy, fluid mechanics and plasma physics, can be interpreted by nonlinear systems of nonlinear partial differential equations (NPDEs) [1,2,3,4,5,6,7,8,9]. Where ψ = ψ( x, y, t) is a complex function, ∗ represents the complex conjugate, a is the second-order dβ dispersion coefficient, b1 and b2 are the self-steepening coefficients, σ is the noise strength and β t = dt is the time derivative of the Brownian motion β(t) This noise may be used as an attempt to describe the impact of neglected terms on the modulating of the NLS equation. This paper is the first to obtain the different kinds of the exact solutions of the 2D-SCNLSE (1) coercive by multiplicative noise. Since our approach is new, namely studying the stochastic equations in the Itô sense by multiplicative noise, we plan to consider the 2D-SCNLSE (1) with other interesting methods in the future work. This article is arranged as follows: In Section 2, we obtain the solitary wave solution by applying three different methods and the stochastic exact solutions of the 2D-SCNLSE.

The Exact Solutions of the 2D-CNLSE

Riccati–Bernoulli Sub-ODE Method

He’s Variational Principle Method

Sine–Cosine Method

Physical Interpretation

The Effect of Multiplicative Noise on the Solutions of the 2D-CNLSE

Conclusions