Stable and unstable time quasi periodic solutions for a system of coupled NLS equations
Analysis of PDEs
2018-09-26 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We prove that a system of coupled nonlinear Schr{\"o}dinger 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 [6]. This is the first example of unstable tori for a 1d PDE.
Keywords
Cite
@article{arxiv.1710.09173,
title = {Stable and unstable time quasi periodic solutions for a system of coupled NLS equations},
author = {Benoît Grébert and Victor Vilaça da Rocha},
journal= {arXiv preprint arXiv:1710.09173},
year = {2018}
}