Asymptotic stability of solitons for the Benjamin-Ono equation

Asymptotic stability of solitons for the Benjamin-Ono equation

Carlos E. Kenig and Yvan Martel

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

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.

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Primary Subjects: 35Q53, 35Q51, 35B40

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

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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1257258098
Zentralblatt MATH identifier: 05663367
Mathematical Reviews number (MathSciNet): MR2590690

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