Electron. J. Differential Equations, Vol. 2021 (2021), No. 41, pp. 1-14.
Lie symmetry analysis and conservation laws for the (2+1)-dimensional Mikhalev equation
Xinyue Li, Yongli Zhang, Huiqun Zhang, Qiulan Zhao
Abstract:
Lie symmetry analysis is applied to the (2+1)-dimensional Mikhal\"ev equation,
which can be reduced to several (1+1)-dimensional partial differential equations with
constant coefficients or variable coefficients. Then we construct exact explicit solutions
for part of the above (1+1)-dimensional partial differential equations. Finally,
the conservation laws for the (2+1)-dimensional Mikhal\"ev equation are constructed
by means of Ibragimov's method.
Submitted October 28, 2020. Published May 7, 2021.
Math Subject Classifications: 35Q53, 37K30;,37K40.
Key Words: (2+1)-dimensional Mikhalev equation; Lie symmetry analysis;
similarity reduction; conservation law; exact solution.
DOI: https://doi.org/10.58997/ejde.2021.41
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Xinyue Li
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: xyli@sdust.edu.cn
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Yongli Zhang
Department of Mathematics and Statistics
Qingdao University
Qingdao, Shandong 266071, China
email: zhangyonglisumili@163.com
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Huiqun Zhang
Department of Mathematics and Statistics
Qingdao University
Qingdao, Shandong 266071, China
email: qddxzhanghq@163.com
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Qiulan Zhao
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: qlzhao@sdust.edu.cn
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