A finite-dimensional integrable system related to a new coupled KdV hierarchy

A new 4×4 isospectral problem with three potentials and the corresponding hierarchy of nonlinear evolution equations are presented. Especially, a new coupled KdV equation is produced. Their generalized bi-Hamiltonian structures are also investigated by using the trace identity. Moreover, a new finite-dimensional Hamiltonian system is given through the nonlinearization of the corresponding Lax pair. Enough conserved integrals, which are in involution and functionally independent, are created by the Lax operator to guarantee Liouville integrability of the Hamiltonian system.