Finite-dimensional Integrable Systems Associated With A Soliton Hierarchy

Under a constraint between the potential and the eigenfunctions, we obtain a class of new finite-dimensional Hamiltonian systems through nonlinearization of Lax pairs. These finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. The associated soli-ton hierarchy is decomposed into two new compatible Hamiltonian systems of ordinary differential equations.