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

doi:10.1088/1674-1056/ab5eff

中国物理B ›› 2020, Vol. 29 ›› Issue (2): 20201-020201.doi: 10.1088/1674-1056/ab5eff

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 下一篇

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

Ping Liu(刘萍), Jie Cheng(程杰), Bo Ren(任博), Jian-Rong Yang(杨建荣)

1 School of Electronic and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China;
2 School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China;
3 Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
4 School of Physics and Electronic Information, Shangrao Normal University, Shangrao 334001, China

收稿日期:2019-07-29 修回日期:2019-11-18 出版日期:2020-02-05 发布日期:2020-02-05
通讯作者: Ping Liu E-mail:liuping49@126.com
基金资助:
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).

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

Ping Liu(刘萍)¹, Jie Cheng(程杰)², Bo Ren(任博)³, Jian-Rong Yang(杨建荣)⁴

1 School of Electronic and Information Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China;
2 School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China;
3 Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
4 School of Physics and Electronic Information, Shangrao Normal University, Shangrao 334001, China

Received:2019-07-29 Revised:2019-11-18 Online:2020-02-05 Published:2020-02-05
Contact: Ping Liu E-mail:liuping49@126.com
Supported by:
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).

摘要/Abstract

摘要： 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.

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

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.

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

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Hj (Classical groups) 02.20.Sv (Lie algebras of Lie groups)

刘萍, 程杰, 任博, 杨建荣. Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation[J]. 中国物理B, 2020, 29(2): 20201-020201.

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[J]. Chin. Phys. B, 2020, 29(2): 20201-020201.

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

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

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