Almost periodic invariant tori for the NLS on the circle
Biasco, Luca1 ; Massetti, Jessica Elisa1 ; Procesi, Michela1
1 Università degli Studi Roma Tre, Italy
Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 711-758.
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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 in [15] 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” à 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.

Reçu le :
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.09.003
Mots-clés : Almost periodic solutions, Nonlinear Schrodinger equation, KAM for PDEs
Biasco, Luca 1 ; Massetti, Jessica Elisa 1 ; Procesi, Michela 1

1 Università degli Studi Roma Tre, Italy 
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Biasco, Luca; Massetti, Jessica Elisa; Procesi, Michela. Almost periodic invariant tori for the NLS on the circle. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 711-758. doi : 10.1016/j.anihpc.2020.09.003. http://www.numdam.org/articles/10.1016/j.anihpc.2020.09.003/

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