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A recently proposed discrete version of the Schrodinger spectral problem isconsidered. The whole hierarchy of differential-difference nonlinear evolutionequations associated to this spectral problem is derived. It is shown that adiscrete version of the KdV, sine-Gordon and Liouville equations are includedand that the so called `inverse' class in the hierarchy is local. The wholeclass of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

A discrete Schr dinger spectral problem and associated evolution equations