The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure
Yue Chao(岳超)a)†, Yang Geng-Wen(杨耕文)b), and Xu Yue-Cai(许曰才)c)
a School of Information Engineering, Taishan Medical University, Taian 271016, China; b Editorial Department of Journal of Luoyang University, Luoyang 471023, China; c School of Adult Education, Shandong University of Science and Technology, Taian 271000, China
Abstract In this paper a type of 9-dimensional vector loop algebra $\tilde{F}$ is constructed, which is devoted to establish an isospectral problem. It follows that a Liouville integrable coupling system of the m-AKNS hierarchy is obtained by employing the Tu scheme, whose Hamiltonian structure is worked out by making use of constructed quadratic identity. The method given in the paper can be used to obtain many other integrable couplings and their Hamiltonian structures.
Received: 24 June 2006
Revised: 06 July 2006
Accepted manuscript online:
Yue Chao(岳超), Yang Geng-Wen(杨耕文), and Xu Yue-Cai(许曰才) The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure 2007 Chinese Physics 16 595
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