English

On small travelling waves to the mass critical fractional NLS

Analysis of PDEs 2017-12-14 v1

Abstract

We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associated profiles in the small mass limit. We therefore recover a situation similar to the one discovered in [Gerard P.; Lenzmann E.; Pocovnicu O.; Rapha\"el, P., A two soliton with transient turbulent regime for the one dimensional cubic half wave, submitted] for the critical case s = 1, but with a completely different asymptotic profile when the mass vanishes.

Keywords

Cite

@article{arxiv.1712.04484,
  title  = {On small travelling waves to the mass critical fractional NLS},
  author = {Ivan Naumkin and Pierre Raphaël},
  journal= {arXiv preprint arXiv:1712.04484},
  year   = {2017}
}