We consider the nonlinear Schrödinger equation of degree five on the circle. We prove the existence of quasi-periodic solutions which bifurcate from “resonant” solutions (already studied by Benoît Grébert and Laurent Thomann) of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect. This is a joint work with Michela Procesi.
KAM for beating solutions of the quintic NLS
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Nom de l'orateur
Emanuele Haus
Etablissement de l'orateur
Università degli Studi di Napoli "Federico II"
Dipartimento di Matematica e Applicazioni "Renato Caccioppoli"
Date et heure de l'exposé
Lieu de l'exposé