Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique
Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique
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DOI：
10.1016/0375-9601(83)90764-8
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发表时间：
1983-04
影响因子：
2.6
通讯作者：
N. C. Freeman;J. Nimmo
中科院分区：
文献类型：
--
作者：
N. C. Freeman;J. Nimmo
Kadomtsev-Petviashvili 方程的众所周知的孤子解是用朗斯基形式的行列式编写的。通过使用这种紧致表示和方程的 Hirota 双线性形式，用初等代数方法证明了 N-孤子解满足演化方程，并且 N 和 N+ 1-孤子解满足相关的 Bäcklund 变换。还给出了这些结果与逆散射方法的本征解以及与 N-孤子解的更常见表示形式的关系。
The well known soliton solutions of the Kadomtsev-Petviashvili equations are written in terms of determinants of Wronskian form. By using this compact representation together with the Hirota bilinear form of the equations, it is demonstrated by elementary algebraic methods that theN-soliton solution satisfies the evolution equation and theNandN+ 1-soliton solutions satisfy the associated Bäcklund transformation. The relation of these results to the eigensolutions of the inverse scattering method and to the more usual representation of theN-soliton solution is also given.