A 2-PARAMETER HIERARCHY OF INTEGRABLE LATTICE EQUATIONS

A new discrete matrix spectral problem with two arbitrary constants is introduced, and the corresponding 2-parameter hierarchy of integrable lattice equations is obtained by discrete zero curvature representation. The resulting integrable lattice equations reduce to the hierarchy of relativistic Toda lattice in rational form for a special choice of the parameters. Moreover, a sub-hierarchy of the resulting integrable lattice equations is discussed. It is shown that each lattice equation in the sub-hierarchy is a Liouville integrable discrete Hamiltonian equation.