3×3矩阵谱问题的约化及约化方程

3×3 Matrix Spectral Problems Reductions and Reduced Evolution Equations

对称群方法对可用ＩＳＴ方法求解的可积系统的完全分类是一种很有效的方法。规范等价系统的解、守恒律等以一种明显的方式联系着，而我们已证明了约化群在规范变换下是不变的，因此对可积系统进行规范分类就非常重要。在本文中，用对称群方法研究了３×３矩阵谱问题的约化枚举及分类，并得到了一些新的约化方程族。

The method of symmetry group is very useful to the complete classification of the sys-tems integrable by IST. For the solutions and conservation laws of gauge equivalance systems are con-nected in obvious ways and we have proved that reduction groups are invariant to classify integrable sys-tems in gauge. In this paper,with the help of symmetry group,the enumeration and classification of re-ductions of 3×3 matrix spectral problems are investigated and the corresponding hierachies of reducedevolution equations are got.