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.

Biasco, L., Massetti, J.E., & Procesi, M. (2020). Almost periodic invariant tori for the NLS on the circle. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE [10.1016/j.anihpc.2020.09.003].

Almost periodic invariant tori for the NLS on the circle

Biasco L.;Massetti J. E.
;
Procesi M.
2020

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 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.
Biasco, L., Massetti, J.E., & Procesi, M. (2020). Almost periodic invariant tori for the NLS on the circle. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE [10.1016/j.anihpc.2020.09.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/377121
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