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]).
Biasco, L., Massetti, J.E., Procesi, M. (2019). Exponential and sub-exponential stability times for the NLS on the circle. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 30(2), 351-364 [10.4171/RLM/850].
Exponential and sub-exponential stability times for the NLS on the circle
Biasco L.;Massetti J. E.;Procesi M.
2019-01-01
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]).| File | Dimensione | Formato | |
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