Three types of generalized Kadomtsev－Petviashvili equations arising from baroclinic potential vorticity equation

doi:10.1088/1674-1056/19/2/020201

Abstract By means of the reductive perturbation method, three types of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP) equations are derived from the baroclinic potential vorticity (BPV) equation, including the modified KP (mKP) equation, standard KP equation and cylindrical KP (cKP) equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.

Keywords: baroclinic potential vorticity equation generalized Kadomtsev--Petviashvili equation symmetry groups approximate solution

Received: 24 March 2009
Revised: 24 July 2009
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Jr	(Partial differential equations)
	02.20.-a	(Group theory)

Fund: Project supported by National Natural Science Foundation of China (Grant Nos. 10735030 and 40775042), Ningbo Natural Science Foundation (Grant No. 2008A610017), National Basic Research Program of China (973 Program) (Grant Nos. 2005CB422301 and 2007CB814800) and K.C. Wong Magna Fund in Ningbo University.

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Zhang Huan-Ping(张焕萍), Li Biao(李彪), Chen Yong (陈勇), and Huang Fei(黄菲) Three types of generalized Kadomtsev－Petviashvili equations arising from baroclinic potential vorticity equation 2010 Chin. Phys. B 19 020201

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Three types of generalized Kadomtsev－Petviashvili equations arising from baroclinic potential vorticity equation

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