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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20201-020201.doi: 10.1088/1674-1056/19/2/020201

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

黄菲¹, 张焕萍², 陈勇³, 李彪⁴

(1)Department of Marine Meteorology, Ocean University of China, Qingdao 266003, China; (2)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; (3)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China;Institute of Theoretical Computing, East China Normal University, Shanghai 200062, China; (4)Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China;Key Laboratory of Mat

收稿日期:2009-03-24 修回日期:2009-07-24 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
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.

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

Zhang Huan-Ping(张焕萍)^a), Li Biao(李彪)^a)d)^†, Chen Yong (陈勇)^a)b), and Huang Fei(黄菲)^c)

^a Nonlinear Science Center and Department of Mathematics, Ningbo University, Ningbo 315211, China; ^b Institute of Theoretical Computing, East China Normal University, Shanghai 200062, China; ^c Department of Marine Meteorology, Ocean University of China, Qingdao 266003, China; ^d Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100190, China

Received:2009-03-24 Revised:2009-07-24 Online:2010-02-15 Published:2010-02-15
Supported by:
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.

摘要/Abstract

摘要： 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.

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.

Key words: baroclinic potential vorticity equation, generalized Kadomtsev--Petviashvili equation, symmetry groups, approximate solution

中图分类号: (Solitons)

05.45.Yv

02.30.Jr (Partial differential equations) 02.20.-a (Group theory)

张焕萍, 李彪, 陈勇, 黄菲. Three types of generalized Kadomtsev－Petviashvili equations arising from baroclinic potential vorticity equation[J]. 中国物理B, 2010, 19(2): 20201-020201.

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[J]. Chin. Phys. B, 2010, 19(2): 20201-020201.

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

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

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