Dynamics of Partial Differential Equations

Volume 16 (2019)

Number 3

An unstable three-dimensional KAM torus for the quintic NLS

Pages: 273 – 293

DOI: https://dx.doi.org/10.4310/DPDE.2019.v16.n3.a3


Nguyen Thuy Trung (Laboratoire de Mathématiques J. Leray, Université de Nantes, France)


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