Decomposition Of Soliton Hierarchy Associated With A Schr(?)dinger Type Spectral Problem

Using the nonlinearization approach of Lax pairs, the soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals is presented, based on which these finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.