English

On the non-existence of local Birkhoff coordinates for the focusing NLS equation

Analysis of PDEs 2018-09-28 v2

Abstract

We prove that there exist potentials so that near them the focusing non-linear Schr\"odinger equation does not admit local Birkhoff coordinates. The proof is based on the construction of a local normal form of the linearization of the equation at such potentials.

Keywords

Cite

@article{arxiv.1807.02455,
  title  = {On the non-existence of local Birkhoff coordinates for the focusing NLS equation},
  author = {T. Kappeler and P. Topalov},
  journal= {arXiv preprint arXiv:1807.02455},
  year   = {2018}
}