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 integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting integrable lattice equations. At last, conservation laws of the hierarchy are presented.