The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method

Wael W Mohammed,Abeer M Albalahi,Farah M Al-Askar,Mahmoud El-Morshedy

doi:10.3390/math10050817

Abstract

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation.

Highlights

Deterministic nonlinear evolution equations (NLEEs) were widely utilized to illustrate some nonlinear phenomena in quantum mechanics, solid-state physics, fluid mechanics, chemical kinematics, plasma physics, the heat flow, optical fibres, etc
Many effective analytical and numerical methods have been proposed by a diverse group of physicists and mathematicians
We demonstrate here the impact of the Wiener process on the analytical solutions of the stochastic (2+1)-dimensional breaking soliton equation (SBSE) (1)

Summary

Introduction

Deterministic nonlinear evolution equations (NLEEs) were widely utilized to illustrate some nonlinear phenomena in quantum mechanics, solid-state physics, fluid mechanics, chemical kinematics, plasma physics, the heat flow, optical fibres, etc. Many authors have obtained the analytical solutions of the deterministic breaking soliton equation by various methods such as the three-wave [23], Hirota bilinear [24],. Our motivation for this work is to acquire the analytical stochastic solutions of the SBSE (1), which has never been considered before in the presence of a stochastic term. To achieve these solutions, we employ the tanh–coth method. Due to the relevance of this equation, which is used to describe the hydrodynamic wave model of shallow-water waves, plasma physics, and the leading flow of fluid, these analytical stochastic solutions are more extensive and crucial in explaining numerous extremely sophisticated physical phenomena.

Tanh–Coth Method

The Impact of Wiener Process on the Solutions of SBSE

Conclusions