A hierarchy of integrable nonlinear lattice equations and its two integrable coupling systems

Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is integrable in the Liouville sense. A few subalgebras of the Lie algebra are constructed from which the corresponding loop algebras can be presented. It follows that the enlarging algebra systems are introduced. Moreover, we construct the two integrable coupling systems with the help of the enlarging algebra systems.