An integrable discretization of KdV at large times

Abstract

An "exact discretization" of the Schroedinger 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.

12 pages

Cited by in corpus (11)

• An Inverse Scattering Transform for the Lattice Potential KdV Equation
• The lattice Schwarzian KdV equation and its symmetries
• A discrete Schrodinger spectral problem and associated evolution equations
• Loop Groups and Discrete KdV Equations
• Multidimensional Inverse Scattering of Integrable Lattice Equations
• Infinitely many conservation laws for the discrete KdV equation
• Negative Volterra flows
• Integrable discretizations of the sine-Gordon equation
• Two New Integrable Lattice Hierarchies Associated With A Discrete Schrodinger Nonisospectral Problem and Their Infinitely Many Conservation Laws
• Spectrum transformation and conservation laws of the lattice potential KdV equation
• Continuous Symmetries of the Lattice Potential KdV Equation