Revista Matemática Iberoamericana


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Volume 25, Issue 3, 2009, pp. 909–970
DOI: 10.4171/RMI/586

Published online: 2009-12-31

Asymptotic stability of solitons for the Benjamin-Ono equation

Carlos E. Kenig[1] and Yvan Martel[2]

(1) University of Chicago, USA
(2) École Polytechnique, Palaiseau, France

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, Y. and Merle, F.: Asymptotic stability of solitons for subcritical generalized KdV equations. Arch. Ration. Mech. Anal. 157 (2001), 219-254], [Martel, Y. and Merle, F.: Asymptotic stability of solitons of the gKdV equations with a general nonlinearity. Math. Ann. 341 (2008), 391-427]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.

Keywords: Benjamin-Ono equation, soliton, asymptotic stability, Liouville theorem

Kenig Carlos, Martel Yvan: Asymptotic stability of solitons for the Benjamin-Ono equation. Rev. Mat. Iberoamericana 25 (2009), 909-970. doi: 10.4171/RMI/586