A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map

Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrablesymplectic map and finite-dimensional integrable systems are givenby nonlinearization method. The binary Bargmann constraint givesrise to a Bäcklund transformation for the resultingintegrable lattice equations. At last, conservation laws of thehierarchy are presented.