| Painlevé Analysis,Soliton Collision and B?cklund Transformation for the (3+1)-Dimensional Variable-Coefficient Kadomtsev–Petviashvili Equation in Fluids or Plasmas |
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| 引用本文： | 解西阳,田播,江彦,仲晖,孙亚,王云坡.Painlevé Analysis,Soliton Collision and B?cklund Transformation for the (3+1)-Dimensional Variable-Coefficient Kadomtsev–Petviashvili Equation in Fluids or Plasmas[J].理论物理通讯,2014(7). |
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| 作者姓名： | 解西阳 田播 江彦 仲晖 孙亚 王云坡 |
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| 基金项目： | Supported by the National Natural Science Foundation of China under Grant No.11272023;the Open Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)under GrantNo.IPOC2013B008;the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02 |
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| 摘 要： | In this paper, we investigate a(3+1)-dimensional generalized variable-coefficient Kadomtsev–Petviashvili equation, which can describe the nonlinear phenomena in fluids or plasmas. Painlev′e analysis is performed for us to study the integrability, and we find that the equation is not completely integrable. By virtue of the binary Bell polynomials,bilinear form and soliton solutions are obtained, and B¨acklund transformation in the binary-Bell-polynomial form and bilinear form are derived. Soliton collisions are graphically discussed: the solitons keep their original shapes unchanged after the collision except for the phase shifts. Variable coefficients are seen to affect the motion of solitons: when the variable coefficients are chosen as the constants, solitons keep their directions unchanged during the collision; with the variable coefficients as the functions of the temporal coordinate, the one soliton changes its direction.
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| 关 键 词： | (+)-dimensional generalized variable-coefficient Kadomtsev–Petviashvili equation in fluids or plasmas Hirota method soliton solutions B¨acklund transformation Bell polynomials |
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