Dynamics on resonant clusters for the quintic non linear Schrödinger equation

Emanuele Haus (1) , Laurent Thomann (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We construct solutions to the quintic nonlinear Schrödinger equation on the circle with initial conditions supported on arbitrarily many different resonant clusters. This is a sequel of a work of Benoît Grébert and the second author.

Mots clés: Nonlinear Schrödinger equation; Resonant normal form; energy exchange

Domaines: Equations aux dérivées partielles [math.AP]

Emanuele Haus, Laurent Thomann. Dynamics on resonant clusters for the quintic non linear Schrödinger equation. Dynamics of Partial Differential Equations, 2013, 10 (2), pp.157--169. ⟨hal-00746080⟩