摘要
Under investigation in this paper is a(3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials,symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, B¨acklund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.
Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials, symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, Backlund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.
基金
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 Grant No.IPOC2013B008
the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
关键词
LAX对
变系数
孤立波解
方程
BACKLUND变换
双线性形式
流体
孤子解
（3 ＋ 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, soliton solutions,B^cklund transformations, symbolic computation
