Exponential Stability Estimates for the 1D NLS

2018/10/15 by Luca, Biasco, Massetti, Jessica Elisa, Procesi, Michela
#35Q55 #37K55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.06440

Abstract

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 prove a rather flexible Birkhoff Normal Form theorem, which implies, e.g., exponential and sub-exponential time estimates in the Sobolev and Gevrey class respectively.

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