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October, 2009 Asymptotic stability of solitons for the Benjamin-Ono equation
Carlos E. Kenig , Yvan Martel
Rev. Mat. Iberoamericana 25(3): 909-970 (October, 2009).

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.

Citation

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Carlos E. Kenig . Yvan Martel . "Asymptotic stability of solitons for the Benjamin-Ono equation." Rev. Mat. Iberoamericana 25 (3) 909 - 970, October, 2009.

Information

Published: October, 2009
First available in Project Euclid: 3 November 2009

zbMATH: 1247.35133
MathSciNet: MR2590690

Subjects:
Primary: 35B40, 35Q51, 35Q53

Rights: Copyright © 2009 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.25 • No. 3 • October, 2009
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