Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation

doi:10.1088/1674-1056/ab5eff

Abstract The famous Kadomtsev-Petviashvili (KP) equation is a classical equation in soliton theory. A Bäcklund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painlevé expansion in this paper. One-parameter group transformations and one-parameter subgroup-invariant solutions for the extended KP equation are obtained. The consistent Riccati expansion (CRE) solvability of the KP equation is proved. Some interaction structures between soliton-cnoidal waves are obtained by CRE and several evolution graphs and density graphs are plotted.

Keywords: Kadomtsev-Petviashvili (KP) equation consistent Riccati expansion symmetry Bäcklund transformation interaction solution

Received: 29 July 2019
Revised: 18 November 2019
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.20.Hj	(Classical groups)
	02.20.Sv	(Lie algebras of Lie groups)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775047，11775146，and 11865013) and the Science and Technology Project Foundation of Zhongshan City, China (Grant No. 2017B1016).

Corresponding Authors: Ping Liu
E-mail: liuping49@126.com

Cite this article:

Ping Liu(刘萍), Jie Cheng(程杰), Bo Ren(任博), Jian-Rong Yang(杨建荣) Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation 2020 Chin. Phys. B 29 020201

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Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation

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