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arXiv · 1609.01684

KAM for beating solutions of the quintic NLS

Emanuele Haus·Michela Procesi
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Abstract

We consider the nonlinear Schr\"{o}dinger equation of degree five on the circle $\mathbb{S}^1 = \mathbb{R}/2\pi$. We prove the existence of quasi-periodic solutions which bifurcate from "resonant" solutions (studied in [14]) 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.

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Emanuele Haus, Michela Procesi. 2016-09-06. KAM for beating solutions of the quintic NLS. https://doi.org/10.1007/s00220-017-2925-7

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