和高阶约束相联系的可积系统

The Integrable System Associated with Higher-order Constraint

对（１＋１）维可积系统，本文在零曲率方程表示理论框架内，给出统一的方法去构造和高阶约束相联系的有限维可积系统，导出这些系统的守恒积分的生成函数，证明它们的可积性，并进而把一族（１＋１）维可积系统中的每一个方程分解为两个可交换的有限维可积的Ｈａｍｉｌｔｏｎ系统。

In the framework of zero-curvature representation theory,an unified method for constructing finite-dimensional integrable Hamiltonian systems(FDIHS)from(1+1)-dimensional integral systems via the higher-order constraints is proposed, the generating function for the integrals of motion and integrability for these FDIHSs are shown. Furthermore each equation inthe hierarchy of(1+1)-dimensional integrable systems is factorized into two commuting FDIHSs.