2+1-维变系数广义Kadomtsev-Petviashvili方程的相似约化

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基金项目: 国家自然科学基金资助项目(19572022);国家攀登计划基金

Similarity Reductions for 2+1-Dimensional Variable Coefficient Generalized Kadomtsev-Petviashvili Equation

Institute of Mathematical Science, Dalian University of Technology, Dalian 116024, P R China

摘要: 借助于MATHEMATICA软件,将直接约化法推广并应用到2+1-维变系数广义Kadomtsev-Petviashvili(VCGKP)方程,获得了VCGKP方程的若干相似约化,其中包括PainleveⅠ型、PainleveⅡ型和PainleveⅣ型的约化.
- 变系数广义Kadomtsev-Petviashvili方程 /
- 直接约化法 /
- 相似约化
Abstract: With the aid of MATHEMATICA,the direct reduction method was extended and applied in 2+1-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation(VCGKPE).As a result,several kinds of similarity reductions for VCGKPE are obtained which contain PainleveⅠ,Painleve Ⅱ and PainleveⅣ reductions.
- variable coefficient generalized Kadomtsev-Petviashvili equation /
- direct reduction method /
- similarity reduction

[1]	Clarkson P A,Kruskal M D.New similarity reductions of the Boussinesq equation[J].J Math Phys,1989,30(10):2201~2212.
[2]	Zhang J F,Zhu Y J,Lin J.Similarity reductions for the Khokhlov-Zabolotskaya equation[J].Commun Theor Phys,1995,22(1):69~74.
[3]	Ruan H Y,Lou S Y.Similarity reductions and Painleve properties for the Kupershmidt equation[J].Commun Theor Phys,1993,20(1):73~80.
[4]	阮航宇,楼森岳.Whitham-Broer-Kaup 浅水波方程的对称性约化[J].物理学报,1992,41(8):1213~1219.
[5]	谷超豪,李翊神,田畴,等.孤立子理论与应用[M].杭州:浙江科学技术出版社,1990.
[6]	Ablowitz M J,Clarkson P A.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].New York:Cambridge University Press,1991.
[7]	Wang M L,Zhou Y B,Li Z B.Application of a homogeneous blance method to exact solutions of nonlinear equations in mathematical physics[J].Phys Lett A,1996,216(1):67~73.
[8]	Lou S Y.Painlev test for the integrable dispersive long wave equations in two space dimensions[J].Phys Lett A,1993,176(1):96~102.

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