Stable and unstable time quasi periodic solutions for a system of coupled NLS equations

Abstract

We prove that a system of coupled nonlinear Schrödinger equations on the torus exhibits both stable and unstable small KAM tori. In particular, the unstable tori are related to a beating phenomena which has been proved recently in Grébert et al (2013 Nonlinearity 26 1361–76). This is the first example of unstable tori for a 1D PDE.