Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system

Huizhang Yang; Wei Liu; Yunmei Zhao; Huizhang Yang; Wei Liu; Yunmei Zhao

doi:10.3934/math.2021065

AIMS Mathematics

2021, Volume 6, Issue 2: 1087-1100. doi: 10.3934/math.2021065

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Research article

Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system

College of Mathematics, Honghe University, Mengzi, Yunnan, 661199, China

Received: 03 August 2020 Accepted: 04 November 2020 Published: 09 November 2020
MSC : 37L20, 35C05, 35Q53

Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived. Furthermore, the similarity variables and symmetry reductions of this new generalized two-component Hunter-Saxton system are derived. Under these Lie symmetry reductions, some exact solutions are obtained by using the symbolic computation. Moreover, a conservation law of this system is presented by using the multiplier approach.
- generalized two-component Hunter-Saxton system,
- Lie symmetry analysis,
- symmetry reductions,
- exact solutions,
- conservation law
Citation: Huizhang Yang, Wei Liu, Yunmei Zhao. Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system[J]. AIMS Mathematics, 2021, 6(2): 1087-1100. doi: 10.3934/math.2021065

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Abstract

Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived. Furthermore, the similarity variables and symmetry reductions of this new generalized two-component Hunter-Saxton system are derived. Under these Lie symmetry reductions, some exact solutions are obtained by using the symbolic computation. Moreover, a conservation law of this system is presented by using the multiplier approach.

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