二次型等式及其多分量可积族的Hamilton结构

The Quadric Form Identity and Hamilton Structure of Multi-component Hierarchy

构造了一个新的Lie代数G，通过选取恰当的基元阶数得到相应的一个loop代数GM，其换位运算非常简便，由此设计一个等谱问题，利用屠格式得到一个新的Liouville可积的多分量Hamilton方程族，并利用二次型等式获得方程族的Hamiltonian结构。此种方法可以广泛使用，获得其他方程族的Hamiltonian结构。

In this paper, a new Lie algebra G is constructed and a corresponding loop algebra GM is obtained by choo sing the proper order of the basic elements and its commutation operation defined is very concise. It follows that an isospectral problem is established and a new Liouville integrable multi-component Hamiltonian hierarchy is obtained by making use of Tu pattern. Also, Hamiltonian structures of the multi-component hierarchy are presented by the quadratic form identity, This method can be generally used and the Hamilton structures of other integrable hierarchies are obtained.