New completely integrable Neumann systems related to the perturbation KdV hierarchy

Using the nonlinearization approach, a class of new finite-dimensional Hamiltonian systems and a class of new finite-dimensional Neumann systems are obtained from the 4 X 4 matrix eigenvalue problem associated with the perturbation KdV hierarchy. The generating functions of integrals of motion and their generators are presented, based on which two classes of finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, involutive solutions of the perturbation KdV hierarchy are given. (C) 2000 Elsevier Science B.V. All rights reserved.