相联于3×3谱问题的可积方程的某些问题(英文)

Some Problems for the Integrable Equations Associated with a3×3 Spectral Problem

本文推导出相联于3×3谱问题的非线性发展方程的五个分系,我们证明了这五个分系的四个都是Liouville可积的,其中一个是纯粹的微分方程,我们还得到了这五分系的Lax算子,并且考虑了相关的算子代数。

In this paper, five hierarchies of the nonlinear evolution equations associated with a 3×3 spectral problem are derived, we prove that four sets of the hierarchies associated with isospectral deformations of the spectral problem are all Liouville integrable, among them one hierarchy. is proved to be pure differential equations. The Lax operators for the five sets of hierarchy are also given and the relevent operator algebra is considered.