Residual symmetry analysis and CRE integrability of the (3 + 1) -dimensional Burgers system

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.

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Symmetry analysis of a (2+1)-D system

Thermal Science ◽

10.2298/tsci1804811w ◽

2018 ◽

Vol 22 (4) ◽

pp. 1811-1822

Author(s):

Yan Wang ◽

Zhong-Zhou Dong

Keyword(s):

Lie Group ◽

Symmetry Analysis ◽

Vector Analysis ◽

Group Method ◽

Lie Group Method ◽

Generalized Symmetry ◽

Symmetry Method ◽

Burgers System

The classical Lie group method and the (2+1)-D generalized symmetry method in vector analysis are adopted to find infinitesimal symmetries for a (2+1)-D generalized Painleve Burgers system, and its various reduced systems are obtained.

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Some new exact solutions of $(3+1)$-dimensional Burgers system via Lie symmetry analysis

Advances in Difference Equations ◽

10.1186/s13662-021-03220-3 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Elnaz Alimirzaluo ◽

Mehdi Nadjafikhah ◽

Jalil Manafian

Keyword(s):

Vector Fields ◽

Nonlinear Differential Equations ◽

Three Dimensional ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Optimal System ◽

Lie Symmetry Analysis ◽

3 Dimensional ◽

New Exact Solutions ◽

Burgers System

AbstractIn this paper, by using the Lie symmetry analysis, all of the geometric vector fields of the $(3+1)$ ( 3 + 1 ) -Burgers system are obtained. We find the 1, 2, and 3-dimensional optimal system of the Burger system and then by applying the 3-dimensional optimal system reduce the order of the system. Also the nonclassical symmetries of the $(3+1)$ ( 3 + 1 ) -Burgers system will be found by employing nonclassical methods. Finally, the ansatz solutions of BS equations with the aid of the tanh method has been presented. The achieved solutions are investigated through two- and three-dimensional plots for different values of parameters. The analytical simulations are presented to ensure the efficiency of the considered technique. The behavior of the obtained results for multiple cases of symmetries is captured in the present framework. The outcomes of the present investigation show that the considered scheme is efficient and powerful to solve nonlinear differential equations that arise in the sciences and technology.

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Enhanced Symmetry Analysis of Two-Dimensional Burgers System

Acta Applicandae Mathematicae ◽

10.1007/s10440-018-0215-9 ◽

2018 ◽

Vol 163 (1) ◽

pp. 91-128 ◽

Cited By ~ 2

Author(s):

Stavros Kontogiorgis ◽

Roman O. Popovych ◽

Christodoulos Sophocleous

Keyword(s):

Symmetry Analysis ◽

Two Dimensional ◽

Burgers System

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Residual Symmetries and Bäcklund Transformations of Strongly Coupled Boussinesq–Burgers System

Symmetry ◽

10.3390/sym11111365 ◽

2019 ◽

Vol 11 (11) ◽

pp. 1365 ◽

Cited By ~ 3

Author(s):

Haifeng Wang ◽

Yufeng Zhang

Keyword(s):

Bäcklund Transformation ◽

Point Symmetry ◽

Backlund Transformation ◽

Nonlocal Symmetry ◽

Linear Superposition ◽

Strongly Coupled ◽

Residual Symmetry ◽

Commutative Subalgebra ◽

Truncated Painlevé Expansion ◽

Burgers System

In this article, we construct a new strongly coupled Boussinesq–Burgers system taking values in a commutative subalgebra Z 2 . A residual symmetry of the strongly coupled Boussinesq–Burgers system is achieved by a given truncated Painlevé expansion. The residue symmetry with respect to the singularity manifold is a nonlocal symmetry. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is obtained with the help of Lie’s first theorem. Further, the linear superposition of multiple residual symmetries is localized to a Lie point symmetry, and a N-th Bäcklund transformation is also obtained.

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