On The Research Of Satsuma-hirota Coupled Kdv Hierarchy And Their Generalized Hamiltonian Structures

By introducing a 4×4 matrix spectral problem with thress potentials,we propose two classes of nonlinear evolution equations. One typical equation in the first class is the coupled KdV equation by Satsuma and Hirota and another equation in the second class. It is shown that the hierarchy possesses the generalized bi-Hamiltonian form with the help of trace identity, finally,we proved the nonlinear evolution equations are Liouville intergle.