Revista Matemática Iberoamericana

Asymptotic stability of solitons for the Benjamin-Ono equation

Carlos E. Kenig and Yvan Martel

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 25, Number 3 (2009), 909-970.

Dates
First available in Project Euclid: 3 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1257258098

Mathematical Reviews number (MathSciNet)
MR2590690

Zentralblatt MATH identifier
1247.35133

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35Q51: Soliton-like equations [See also 37K40] 35B40: Asymptotic behavior of solutions

Keywords
Benjamin-Ono equation soliton asymptotic stability Liouville theorem

Citation

Kenig, Carlos E.; Martel, Yvan. Asymptotic stability of solitons for the Benjamin-Ono equation. Rev. Mat. Iberoamericana 25 (2009), no. 3, 909--970. https://projecteuclid.org/euclid.rmi/1257258098


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