A nonconfocal generator of involutive systems and three associated soliton hierarchies
A nonconfocal generator of involutive systems and three associated soliton hierarchies
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DOI：
10.1063/1.529156
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发表时间：
1991-09
影响因子：
1.3
通讯作者：
C. Cao;X. Geng
中科院分区：
文献类型：
--
作者：
C. Cao;X. Geng
利用作者提出的特征值问题的非线性化方法，得到了不少新的有限维可积系统。几乎所有与之相关的对合系统都是由共焦生成元生成的：Γk =∑Nj= 1'（λk−λj）−1 B2kj，Bkj =pkqj −pjqk。本文找到了一个非共焦生成元Γk =∑Nj= 1'（λ2k−λ2j）−1 [（λk−λj）2A2kj+e（λk+λj）2B2kj]，Akj =pkpj +eqkqj，由此得到了一些新的可积系统和孤子族.
Quite a few new finite‐dimensional integrable systems have been obtained by the nonlinearization procedure of eigenvalue problems suggested by the author. Almost all of their associated involutive systems are generated from a confocal generator: Γk =∑Nj=1’(λk−λj)−1 B2kj, Bkj =pkqj −pjqk. In the present paper, a nonconfocal generator Γk =∑Nj=1’(λ2k−λ2j)−1 [(λk−λj)2A2kj+e(λk+λj)2 B2kj], Akj =pkpj +eqkqj is found, from which some new integrable systems and soliton hierarchies are obtained.