Abstract
Discrete integrable coupling hierarchies of two existing integrable lattice families are derived from a four by four discrete matrix spectral problem. It is shown that the obtained integrable coupling hierarchies respectively corresponds to negative and positive power expansions of the Lax operator with respect to the spectral parameter. Then, the Hamiltonian form of the negative integrable coupling hierarchy is constructed by using the discrete variational identity. Finally, Liouville integrability of each obtained discrete Hamiltonian system is demonstrated.
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