Drinfeld-Sokolov-Satsuma-Hirota方程族及其广义双Hamiltonian结构

摘要

A hierarchy of nonlinear evolution equations was derived from a matrix spectral problem with two potentials, in which a typical member was the Drinfeld-Sokolov-Satsuma-Hirota equation . It was shown that the hierarchy of nonlinear evolution equations possessed the generalized bi-Hamiltonian structures and was completely integrable in the Liuovlle sense.%基于带有两个位势的4×4矩阵谱问题,导出一族非线性演化方程,其中一个典型成员是Drirfeld-Sokolov-Satsuma-Hirota方程.进而证明了这族方程具有广义双Hamiltonian结构并且在Liuovlle意义下是完全可积的.