Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation |
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Authors: | Wang Jia and Li Biao |
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Institution: | Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; MM Key Laboratory, Chinese Academy of Sciences, Beijing 100190, China |
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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. |
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Keywords: | symmetry general symmetry
groups coupled KP equation |
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