Asymptotic stability of solitons for the Benjamin-Ono equation

@inproceedings{Kenig2008AsymptoticSO,
  title={Asymptotic stability of solitons for the Benjamin-Ono equation},
  author={Carlos E. Kenig and Yvan Martel},
  year={2008}
}
In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [16], [18]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.