Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations

Details Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations Asymptotic behavior of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations

2004-09-06

arxiv.org/abs/nlin/0409009v1

Nonlinear Sciences

Pattern Formation and Solitons

13 pages, 4 figures

Scientific paper

10.1088/0951-7715/18/4/022

We show decay estimates for the propagator of the discrete Schr\"odinger and Klein-Gordon equations in the form $\norm{U(t)f}{l^\infty}\leq C (1+|t|)^{-d/3}\norm{f}{l^1}$. 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 $l^p$ norms. The analytical decay estimates are corroborated with numerical results.

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