A Method of Analysing Soliton Equations by Bilinearization
A Method of Analysing Soliton Equations by Bilinearization
复制标题
孤子方程双线性化分析方法
DOI：
10.1143/jpsj.48.639
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发表时间：
1980
影响因子：
1.7
通讯作者：
S. Oishi
中科院分区：
文献类型：
--
作者：
S. Oishi
近年来，利用Hirota的双线性形式导出了一些孤子方程的一类新的解（S. Oishi: J. Phys.）。Soc。第47号（1979）1341号)。这些解表示波纹背景下的孤子，称为广义孤子解。本文证明了Korteweg-de Vries方程和Kadomtsev-Petviashvili方程的广义孤子解可以转化为Gel'fand-Levitan-Marchenko积分方程的Fredholm行列式的一种形式。利用这一结果，阐明了Hirota方法与逆谱法之间的关系。此外，还证明了这两个方程的初值问题可以用它们的广义孤子解来求解。
Recently, a class of new solutions have been derived for a number of soliton equations using Hirota's bilinear forms of these soliton equations (S. Oishi: J. Phys. Soc. Jpn. 47 (1979) 1341). These solutions express solitons in a background of ripples, and are named generalized soliton solutions. In this paper, it is shown that the generalized soliton solutions for the Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation can be transformed into a form of Fredholm's determinants of the Gel'fand-Levitan-Marchenko integral equation. Using this result, relationship between Hirota's method and the inverse spectral method is clarified. Moreover, it is also shown that the initial value problems for these two equations can be solved using their generalized soliton solutions.