Almost periodic invariant tori for the NLS on the circle

  • Jessica Elisa Massetti

    Università degli Studi Roma Tre, Italy
  • Michela Procesi

    Università degli Studi Roma Tre, Italy
  • Luca Biasco

    Università degli Studi Roma Tre, Italy
Almost periodic invariant tori for the NLS on the circle cover

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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.

Cite this article

Jessica Elisa Massetti, Michela Procesi, Luca Biasco, Almost periodic invariant tori for the NLS on the circle. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 711–758

DOI 10.1016/J.ANIHPC.2020.09.003