Linear integral equations, infinite matrices, and soliton hierarchies
Linear integral equations, infinite matrices, and soliton hierarchies
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DOI：
10.1063/1.5046684
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发表时间：
2017-03
影响因子：
1.3
通讯作者：
Wei-jie Fu;F. Nijhoff
中科院分区：
文献类型：
--
作者：
Wei-jie Fu;F. Nijhoff
提出了一个构造孤子方程族的系统框架。这是通过考虑标量线性积分方程及其表示的无限矩阵，从而产生所有的（2+1）-和（1+1）-维孤子与标量微分谱问题的层次。所得到的孤子族，包括三浦型变换，$\tau$-功能，Lax对以及孤子解的可积性特征，也来自在此框架内。
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all (2+1)- and (1+1)-dimensional soliton hierarchies associated with scalar differential spectral problems. The integrability characteristics for the obtained soliton hierarchies, including Miura-type transforms, $\tau$-functions, Lax pairs as well as soliton solutions, are also derived within this framework.