Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials

@inproceedings{Spiridonov1994DiscreteDT,
  title={Discrete Darboux transformations, the discrete-time Toda lattice, and the Askey-Wilson polynomials},
  author={Vyacheslav Pavlovich Spiridonov and Alexei S. Zhedanov},
  year={1994}
}
Consequences of the Darboux transformations for the finite-difference Schrodinger equations and three-term recurrence relations for orthogonal polyno- mials are considered. An equivalence of the chain of these transformations, or discrete dressing chain, to the discrete-time Toda lattice is established. A more fundamental discrete-time Volterra lattice consisting of one simple difference- difference nonlinear equation is found. Some simple similarity reductions of these lattices are described… CONTINUE READING

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