An unstable three-dimensional KAM torus for the quintic NLS

We consider the quintic nonlinear Schrödinger equation on the circle. By applying a Birhoff procedure and a KAM theorem, we exhibit a three-dimensional invariant torus that is linearly unstable. In comparison, we also prove that two-dimensional tori are always linearly stable.

Keywords

unstable KAM torus, quintic NLS, Hamiltonian systems, nonlinear PDE, KAM theory

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The author is partially supported by the grant BeKAM ANR-15-CE40-0001-02, and by the Centre Henri Lebesgue, ANR-11-LABX-0020-01.

Received 11 February 2019

Published 30 August 2019