A discrete Schrodinger spectral problem and associated evolution   equations
  A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited. 
M. Boiti (1), M. Bruschi (2), F. Pempinelli (1) and B. Prinari (1)   ((1) Dipartimento di Fisica dell'Universita` and Sezion...