Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations

Authors

Atanas Stefanov
PG Kevrekidis, University of Massachusetts - AmherstFollow

Publication Date

2005

Journal or Book Title

http://iopscience.iop.org/0951-7715

Abstract

We show decay estimates for the propagator of the discrete Schrödinger and Klein–Gordon equations in the form {{\| {U(t)f} \|}_{{l^\infty}}} \leq C (1+|t|)^{-d/3}{{\| {f} \|}_{{l^1}}} . This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant lp norms. The analytical decay estimates are corroborated with numerical results.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://iopscience.iop.org/0951-7715/18/4/022/

Pages

1841-

Volume

18

Issue

4

Recommended Citation

Stefanov, Atanas and Kevrekidis, PG, "Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations" (2005). http://iopscience.iop.org/0951-7715. 1145.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1145