Super-exponential stability estimate for the nonlinear Schrödinger equation

In this paper, we study the long-time stability of solutions for the 1-dimensional nonlinear Schrödinger equation (NLS) on the torus. Precisely, we prove the super-exponential long time stability of solutions with initial data in some modified Sobolev space. This generalizes the exponential long tim...

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Bibliographic Details
Published in:Journal of functional analysis 2022-12, Vol.283 (12), p.109682, Article 109682
Main Authors: Cong, Hongzi, Mi, Lufang, Shi, Yunfeng
Format: Article
Language:English
Subjects:
1-Dimensional nonlinear Schrödinger equation
Birkhoff normal form
Nonresonant conditions
Super-exponential long time stability
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Summary:In this paper, we study the long-time stability of solutions for the 1-dimensional nonlinear Schrödinger equation (NLS) on the torus. Precisely, we prove the super-exponential long time stability of solutions with initial data in some modified Sobolev space. This generalizes the exponential long time stability result of Biasco-Massetti-Procesi ([2020, CMP]). The main new ingredient here lies on the key observation of some tame type inequality.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2022.109682