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Exponential and sub-exponential stability times for the NLS on the circle

descriptionPublicationkeyboard_double_arrow_right Article 21 Jun 2019 Italy Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Rendiconti Lincei, Matematica e Applicazioni, volume 30, pages 351-364 (issn: 1120-6330, eissn: 1720-0768,

Authors: Biasco, L.; Massetti, J. E.; Procesi, M.;

doi: 10.4171/rlm/850

handle: 2108/360703 , 11590/359610

Exponential and sub-exponential stability times for the NLS on the circle

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Abstract

In this note we study stability times for a family of parameter dependent nonlinear Schrödinger equations on the circle, close to the origin. Imposing a suitable Diophantine condition (first introduced by Bourgain), we state a rather flexible Birkho¤ Normal Form theorem, which implies, e.g., exponential and sub-exponential time estimates in the Sobolev and Gevrey class respectively. Complete proofs are given elsewhere (see [BMP18]).

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Italy

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Keywords

almost global existence, Settore MAT/05, nonlinear Schrodinger equation, Birkhoff Normal Form, Almost global existence; Birkhoff Normal Form; Nonlinear Schrödinger equation

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