Boiti, M.; Bruschi, M.; Pempinelli, F.; Prinari, B. A discrete Schrödinger spectral problem and associated evolution equations. (English) Zbl 1067.39032 J. Phys. A, Math. Gen. 36, No. 1, 139-149 (2003). The hierarchies of differential-difference equations related to the spectral problem \[ \psi(n+ 2)+ q(n)\psi(n+1)= \lambda\psi(n) \] which includes the new discrete integrable version found in the discrete sine-Gordon and Liouville equations, are constructed. Finally, a Darboux transformation \(\widetilde\psi= D\psi\), where \(D\) is an opportune shift operator depending on \(q\) and \(\widetilde q\) related to spectral problem \(\widetilde L\widetilde\psi= \lambda\widetilde\psi\) with \(L'(n,t)= E^2+\widetilde q(n,\psi)E'\) is also introduded. Reviewer: B. M. Agrawal (Gwalior) Cited in 7 Documents MSC: 39A12 Discrete version of topics in analysis 39A70 Difference operators 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems Keywords:discrete Schrödinger spectral problem; evolution equations; sine-Gordon equation; Liouville equations; Darboux transformation; differential difference equations PDFBibTeX XMLCite \textit{M. Boiti} et al., J. Phys. A, Math. Gen. 36, No. 1, 139--149 (2003; Zbl 1067.39032) Full Text: DOI arXiv