A discrete Schrodinger spectral problem and associated evolution equations
M. Boiti, M. Bruschi, F. Pempinelli, B. Prinari
Abstract
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.
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