Dispersive estimates for 1D discrete Schrödinger and Klein–Gordon equations

Abstract

We derive the long-time asymptotics for solutions of the discrete 1D Schrödinger and Klein–Gordon equations.

Keywords:

• Discrete Schrödinger and Klein–Gordon equations
• Lattice
• Cauchy problem
• Long-time asymptotics

Keywords:

• 2000 Mathematics Subject Classifications: 39A11
• 35L10

Acknowledgments

The authors thank very much B. Vainberg for fruitful discussions. A.I.K. was supported partly by Faculty of Mathematics of Vienna University, Max-Planck Institute for Mathematics in the Sciences (Leipzig), and Wolfgang Pauli Institute. E.A.K. was supported partly by research grant of RFBR-NNIO (no. 01-01-04002) and the FWF project “Asymptotics and Attractors of Hyperbolic Equations” (FWF P-16105-N05).