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 isshown 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.Thebinary Bargmann constraint gives rise to a B(a|¨)cklund transformation for the resulting integrable lattice equations.Atlast,conservation laws of the hierarchy are presented.