An integrable coupling family of Merola–Ragnisco–Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family

An integrable coupling family of Merola–Ragnisco–Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation.