Abstract
Some new nonlinear differential-difference integrable hierarchies associated with a properly discrete spectral problem are obtained. The special cases of the proposed differential-difference integrable hierarchies are discussed. The Ablowitz-Ladik discretization of the NLS equation, the discrete modified KdV equation, the modified Toda lattice, the relativistic Toda lattice, and some other lattice soliton equations obtained by Suris are the special examples of novel differential-difference integrable hierarcies.
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