A hierarchy of Liouville integrable lattice equations and its integrable coupling systems

A new discrete two-by-two matrix spectral problem with two potentials is introduced followed by a hierarchy of integrable lattice equations obtained through discrete zero curvature equations It is shown that the Hamiltonian structures of the resulting integrable lattice equations are established by virtue of the trace identity Furthermore based on a discrete four-by-four matrix spectral problem the discrete integrable coupling systems of the resulting hierarchy are obtained Then with the variational identity the Hamiltonian structures of the obtained integrable coupling systems are established Finally the resulting Hamiltonian systems are proved to be all Liouville Integrable (C) 2010 Elsevier BV All rights reserved