An extended Merola-Ragnisco-Tu lattice integrable hierarchy and infinite conservation laws

By means of the zero -curvature equation and Lenard recursive operators, a novel differentialdifference integrable hierarchy is derived, which is related to a discrete 3 x 3 matrix spectral problem with five potentials. The first nontrivial member in this hierarchy under specific reduction is the Merola-Ragnisco-Tu lattice equation whose continuum limit is the nonlinear Schrodinger equation. The infinite conservation laws of the first two nontrivial members in the hierarchy, namely, the extended Merola-Ragnisco-Tu lattice equation and its high -order generalization are constructed with the help of two Ricatti-type equations and the spectral parameter expansions.