Dynamics of Partial Differential Equations
Volume 16 (2019)
An unstable three-dimensional KAM torus for the quintic NLS
Pages: 273 – 293
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.
unstable KAM torus, quintic NLS, Hamiltonian systems, nonlinear PDE, KAM theory
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