Geometric & Functional Analysis GAFA

, Volume 11, Issue 1, pp 74–123 | Cite as

Instability of solitons for the critical generalized Korteweg—de Vries equation

  • Y. Martel
  • F. Merle

Abstract.

We prove in this paper the instability of the solitons for the critical generalized Korteweg—de Vries equation. We obtain this result by a qualitative study of the solution close to the soliton and obtain a large set of initial data giving the instability. This study is a step towards the existence and description of blow up solutions.

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • Y. Martel
    • 1
  • F. Merle
    • 2
  1. 1.Département de Mathématiques, Université de Cergy—Pontoise, 2 avenue Adolphe Chauvin, BP 222, 95302 Cergy—Pontoise, FranceFR
  2. 2.Département de Mathématiques, Université de Cergy—Pontoise, 2 avenue Adolphe Chauvin, BP 222, 95302 Cergy—Pontoise, France, and Institut Universitaire de FranceFR

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