中国物理B ›› 2009, Vol. 18 ›› Issue (6): 2109-2114.doi: 10.1088/1674-1056/18/6/001

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Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

李彪1, 王佳2   

  1. (1)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China;MM Key Laboratory, Chinese Academy of Sciences, Beijing 100190, China; (2)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China
  • 收稿日期:2008-09-26 修回日期:2008-10-27 出版日期:2009-06-20 发布日期:2009-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10747141 and 10735030), National Basic Research Program of China (Grant No 2007CB814800), Natural Science Foundations of Zhejiang Province of China (Grant No 605408), Ningbo Natural Science Foundation (Grant Nos 2007A610049 and 2008A610017) and K. C. Wong Magna Fund in Ningbo University.

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

Wang Jia(王佳)a) and Li Biao(李彪)a)b)†   

  1. a Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; b MM Key Laboratory, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2008-09-26 Revised:2008-10-27 Online:2009-06-20 Published:2009-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10747141 and 10735030), National Basic Research Program of China (Grant No 2007CB814800), Natural Science Foundations of Zhejiang Province of China (Grant No 605408), Ningbo Natural Science Foundation (Grant Nos 2007A610049 and 2008A610017) and K. C. Wong Magna Fund in Ningbo University.

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摘要： In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.

关键词: symmetry, general symmetry groups, coupled KP equation

Abstract: In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.

Key words: symmetry, general symmetry groups, coupled KP equation

中图分类号:  (Solitons)

  • 05.45.Yv
02.10.Ud (Linear algebra) 02.20.Hj (Classical groups) 02.20.Sv (Lie algebras of Lie groups)