On asymptotic stability of standing waves of discrete Schrödinger equation in $\Bbb Z$
| dc.creator | Cuccagna, Scipio | |
| dc.creator | Tarulli, Mirko | |
| dc.date | 2008-08-14 | |
| dc.date | 2009-03-25 | |
| dc.date.accessioned | 2026-07-07T12:55:54Z | |
| dc.date.available | 2026-07-07T12:55:54Z | |
| dc.description | We prove an analogue of a classical asymptotic stability result of standing waves of the Schrödinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi and it involves a discrete Schrödinger operator H. The decay rates on the potential are less stringent than in Mizumachi, since we require for the potential $q\in \ell ^{1,1}$. We also prove $|e^{itH}(n,m)|\le C < t > ^{-1/3}$ for a fixed $C$ requiring, in analogy to Goldberg and Schlag only $q\in \ell ^{1,1}$ if $H$ has no resonances and $q\in \ell ^{1,2}$ if it has resonances. In this way we ease the hypotheses on H contained in Pelinovsky and Stefanov, which have a similar dispersion estimate. | |
| dc.description | This is the revised version, to appear on SIAM Jornal of mathematical Analysis | |
| dc.identifier | https://arxiv.org/abs/0808.2024 | |
| dc.identifier | http://arxiv.org/abs/0808.2024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224407 | |
| dc.subject | Analysis of PDEs | |
| dc.title | On asymptotic stability of standing waves of discrete Schrödinger equation in $\Bbb Z$ | |
| dc.type | text |