New interaction solutions of the Kadomtsev-Petviashvili equation

doi:10.1088/1674-1056/23/10/100201

›› 2014, Vol. 23 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/23/10/100201

• GENERAL • 下一篇

New interaction solutions of the Kadomtsev-Petviashvili equation

刘希忠^a, 俞军^a, 任博^a, 杨建荣^b

a Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
b Department of Physics and Electronics, Shangrao Normal University, Shangrao 334001, China

收稿日期:2014-01-24 修回日期:2013-04-08 出版日期:2014-10-15 发布日期:2014-10-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11347183, 11275129, 11305106, 11405110, and 11365017) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y7080455 and LQ13A050001).

New interaction solutions of the Kadomtsev-Petviashvili equation

Liu Xi-Zhong (刘希忠)^a, Yu Jun (俞军)^a, Ren Bo (任博)^a, Yang Jian-Rong (杨建荣)^b

a Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China;
b Department of Physics and Electronics, Shangrao Normal University, Shangrao 334001, China

Received:2014-01-24 Revised:2013-04-08 Online:2014-10-15 Published:2014-10-15
Contact: Yu Jun E-mail:junyu@usx.edu.cn
About author:02.30.Jr; 02.30.Ik; 05.45.Yv; 47.35.Fg
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11347183, 11275129, 11305106, 11405110, and 11365017) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y7080455 and LQ13A050001).

摘要/Abstract

摘要： The residual symmetry relating to the truncated Painlevé expansion of the Kadomtsev-Petviashvili (KP) equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, new symmetry reduction solutions for the KP equation are obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves are obtained, which are hard to find by other traditional methods.

关键词: Kadomtsev-Petviashvili equation, localization procedure, residual symmetry, Bä, cklund transformation, symmetry reduction solution

Abstract: The residual symmetry relating to the truncated Painlevé expansion of the Kadomtsev-Petviashvili (KP) equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, new symmetry reduction solutions for the KP equation are obtained based on the general form of Lie point symmetry for the prolonged system. In this way, the interaction solutions between solitons and background waves are obtained, which are hard to find by other traditional methods.

Key words: Kadomtsev-Petviashvili equation, localization procedure, residual symmetry, Bäcklund transformation, symmetry reduction solution

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems) 05.45.Yv (Solitons) 47.35.Fg (Solitary waves)

刘希忠, 俞军, 任博, 杨建荣. New interaction solutions of the Kadomtsev-Petviashvili equation[J]. , 2014, 23(10): 100201-100201.

Liu Xi-Zhong (刘希忠), Yu Jun (俞军), Ren Bo (任博), Yang Jian-Rong (杨建荣). New interaction solutions of the Kadomtsev-Petviashvili equation[J]. Chin. Phys. B, 2014, 23(10): 100201-100201.


[27]	Cheng Y and Li Y S 1991 Phys. Lett. A 157 22 doi: 10.1016/0375-9601(91)90403-U

[1]	Miller R E and Tadmor E B 2009 Modell. Simul. Mater Sci. Eng. 17 053001 doi: 10.1088/0965-0393/17/5/053001

[28]	Zeng Y B, Ma W X and Lin R L 2000 J. Math. Phys. 41 5453 doi: 10.1063/1.533420

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New interaction solutions of the Kadomtsev-Petviashvili equation

New interaction solutions of the Kadomtsev-Petviashvili equation

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