English

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}
}