Asymptotic stability of solitons for the Benjamin-Ono equation

By Carlos E. Kenig, Yvan Martel. 2008

68 citations recorded by the source corpus.

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 Martel and Merle (arXiv:0706.1174v2). As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e2cedd73dc4ea7d969c37e4a203d431207b080d7

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In Mathematical Physics

1. Carlos E. Kenig
2. A. Ionescu
3. D. Tataru
4. Terence Tao
5. Zihua Guo
6. Luc Molinet
7. B. Dodson
8. J. Krieger

In Statistical and Nonlinear Physics

1. A. Ionescu
2. Carlos E. Kenig
3. D. Tataru
4. Terence Tao
5. J. Krieger
6. Wilhelm Schlag
7. Luc Molinet
8. B. Dodson

Citations in the corpus

• Global well-posedness of the KP-I initial-value problem in the energy space (2007, background): “Moreover, the more subtle question of asymptotic stability, as in [21, 22, 18 ], can also be naturally posed in the energy space.”