A hierarchy of nonlinear lattice soliton equations, its integrable coupling systems and infinitely many conservation laws

A hierarchy of nonlinear integrable lattice soliton equations is derived from a discrete spectral problem. The lattice hierarchy is proved to have discrete zero curvature representation. Moreover, it is shown that the hierarchy is completely integrable in the Liouville sense. Further, we construct integrable couplings of the resulting hierarchy through an enlarging algebra system X∼. At last, infinitely many conservation laws of the hierarchy are presented.