M Boiti et al 2001 Inverse Problems 17 515 doi:10.1088/0266-5611/17/3/310
M Boiti1, F Pempinelli1, B Prinari1 and A Spire2
Show affiliationsAn `exact discretization' of the Schrödinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)
Issue 3 (June 2001)
Received 16 January 2001, in final form 14 March 2001
M Boiti et al 2001 Inverse Problems 17 515
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