Almost periodic invariant tori for the NLS on the circle

2019/03/18 by Luca Biasco, Jessica Elisa Massetti, Biasco, Luca +3 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1903.07576

44 pages

arxiv created 2020/01/08 · arxiv updated 2020/01/09

Abstract

In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain (2005) on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract "counter-term theorem" `a la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find "many more" almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.

Cited by

• On almost periodic solutions to NLS without external parameters
• The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation

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