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.
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
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/