Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation
Wang Jia(王佳)a) and Li Biao(李彪)a)b)†
a Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; bMM Key Laboratory, Chinese Academy of Sciences, Beijing 100190, China
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.
Received: 26 September 2008
Revised: 27 October 2008
Accepted manuscript online:
Fund: 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.
Cite this article:
Wang Jia(王佳) and Li Biao(李彪) Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation 2009 Chin. Phys. B 18 2109
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