Revista Matemática Iberoamericana
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Published online: 2009-12-31
Asymptotic stability of solitons for the Benjamin-Ono equationCarlos E. Kenig and Yvan Martel (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