We prove an analogue of a classical asymptotic stabilityresult of standing waves of the Schrodinger equation originatingin work by Soffer and Weinstein. Specifically, our result is atransposition on the lattice Z of a result by Mizumachi and it involves a discrete Schr\"odinger operator H=-\Delta +q . The decay rates on the potential are less stringent thanin Mizumachi. We also prove |e^{itH}(n,m)|\le C \langle t \rangle ^{-1/3} for a fixed $C$
On asymptotic stability ofstanding waves of discrete Schr\"odinger equation in Z / Cuccagna, Scipio; M., Tarulli. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 41:(2009), pp. 861-885.
On asymptotic stability ofstanding waves of discrete Schr\"odinger equation in Z
CUCCAGNA, Scipio;
2009
Abstract
We prove an analogue of a classical asymptotic stabilityresult of standing waves of the Schrodinger equation originatingin work by Soffer and Weinstein. Specifically, our result is atransposition on the lattice Z of a result by Mizumachi and it involves a discrete Schr\"odinger operator H=-\Delta +q . The decay rates on the potential are less stringent thanin Mizumachi. We also prove |e^{itH}(n,m)|\le C \langle t \rangle ^{-1/3} for a fixed $C$
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