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Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations

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An Erratum to this article was published on 01 April 2002

Abstract:

We prove in this paper the asymptotic completeness of the family of solitons in the energy space for generalized Korteweg-de Vries equations in the subcritical case (this includes in particular the KdV equation and the modified KdV equation). This result is obtained as a consequence of a rigidity theorem on the flow close to a soliton up to a scaling and a translation, which has its own interest. The proofs use some tools introduced in a previous paper to prove similar results in the case of critical generalized KdV equation.

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Authors and Affiliations

  1. Université de Cergy–Pontoise¶Département de Mathématiques¶2, av. Adolphe Chauvin¶95302 Cergy–Pontoise, France¶e-mail: yvan.martel@math.u-cergy.fr, , , , , , FR

    Yvan Martel

  2. Université de Cergy–Pontoise¶Département de Mathématiques¶2, av. Adolphe Chauvin¶95302 Cergy–Pontoise, France¶e-mail: frank.merle@math.u-cergy.fr, , , , , , FR

    Frank Merle

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  1. Yvan Martel
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  2. Frank Merle
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Accepted December 1, 2000¶Published online April 3, 2001

An erratum to this article is available at http://dx.doi.org/10.1007/s002050200192.

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Martel, Y., Merle, F. Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations. Arch. Rational Mech. Anal. 157, 219–254 (2001). https://doi.org/10.1007/s002050100138

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