A discrete Schrodinger spectral problem and associated evolution equations

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.

14 pages, LaTeX2e

References in corpus (2)

• An integrable discretization of KdV at large times
• Integrable discretizations of the sine-Gordon equation

Cited by in corpus (5)

• Continuous Symmetries of Difference Equations
• Infinitely many conservation laws for the discrete KdV equation
• Negative Volterra flows
• Two New Integrable Lattice Hierarchies Associated With A Discrete Schrodinger Nonisospectral Problem and Their Infinitely Many Conservation Laws
• Discrete Crum's Theorems and Integrable Lattice Equations