Abstract
By means of the zero-curvature equation and Lenard recursive operators, a novel differential-difference integrable hierarchy is derived, which is related to a discrete 3 × 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 Schrödinger 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.
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