Residual Symmetries and Bäcklund Transformations of (2 + 1)-Dimensional Strongly Coupled Burgers System

Haifeng Wang,Yufeng Zhang

doi:10.1155/2020/6821690

Haifeng Wang, Yufeng Zhang

Open Access

https://doi.org/10.1155/2020/6821690

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Abstract

In this article, we mainly apply the nonlocal residual symmetry analysis to a (2 + 1)-dimensional strongly coupled Burgers system, which is defined by us through taking values in a commutative subalgebra. On the basis of the general theory of Painlevé analysis, we get a residual symmetry of the strongly coupled Burgers system. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is derived by Lie’s first theorem. Further, the linear superposition of the multiple residual symmetries is localized to a Lie point symmetry, and an N-th Bäcklund transformation is also obtained.

Highlights

Nonlinear partial differential equations have wide applications in the field of physical science, engineering, and other applied disciplines, e.g., nonlinear optics [1,2,3,4], fluid flows [5,6,7], plasma physics [8, 9], excitable media, and so on [10,11,12,13,14]
Burgers equation 푝 = 2푝푝 + 푝 is a very important nonlinear partial differential equation occurring in various areas of applied sciences, such as fluid mechanics [15], nonlinear acoustics [15], gas dynamics, and traffic flow [16]
In [34, 35], the authors concerned with the application of the nonlocal residual symmetry analysis to (2 + 1)-dimensional Burgers system, which has the form as follows: 푝 = 푝푝 + 푎푟푝 + 푏푝 + 푎푏푝, (1a)

Summary

Haifeng Wang and Yufeng Zhang

Received 1 September 2019; Revised 1 October 2019; Accepted 19 October 2019; Published 23 January 2020. We mainly apply the nonlocal residual symmetry analysis to a (2 + 1)-dimensional strongly coupled Burgers system, which is defined by us through taking values in a commutative subalgebra. On the basis of the general theory of Painlevé analysis, we get a residual symmetry of the strongly coupled Burgers system. En, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. A Bäcklund transformation is derived by Lie’s first theorem. The linear superposition of the multiple residual symmetries is localized to a Lie point symmetry, and an -th Bäcklund transformation is obtained

Introduction

Conclusion and Discussion