一类耦合非线性扩散方程及Liouville完全可积系统

A Hierarchy of Coupled Nonlinear Diffusion Equations and Liouville Completely Integrable Systems

本文引入了一个保谱问题，并导出了相应的耦合非线性演化方程族，得到了两个新的Ｌｉｏｕｖｉｌｌｅ意义下的有限维完全可积系统．

An isospectral problem is proPOsed. The corresponding hierarchy of couplednonlinear evolution equations is derived, they are extensions of the hierarchy of nonlinear diffusion equations. Two new hierarchies of finite - dimensional completely integrable systemsin the liouviue sense are obtained, one of which is the spatial and time parts of nonlineariedLax pairs of the hierarchy of coupled evolution equations.