In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov’s method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving the Bäcklund transformation. The method of constructing lump-type solutions of integrable equations by means of Bäcklund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.
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October 2017
Research Article|
October 30 2017
Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system
Zhonglong Zhao;
Zhonglong Zhao
a)
1
Department of Mathematics, Harbin Institute of Technology
, Harbin 150001, China
2
Department of Mathematics, University of British Columbia
, Vancouver, British Columbia V6T 1Z2, Canada
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Bo Han
Bo Han
1
Department of Mathematics, Harbin Institute of Technology
, Harbin 150001, China
Search for other works by this author on:
a)
Author to whom correspondence should be addressed: zhaozlhit@163.com and zhaozl@alumni.ubc.ca
J. Math. Phys. 58, 101514 (2017)
Article history
Received:
September 07 2017
Accepted:
October 06 2017
Citation
Zhonglong Zhao, Bo Han; Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. J. Math. Phys. 1 October 2017; 58 (10): 101514. https://doi.org/10.1063/1.5003802
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