Geometric & Functional Analysis GAFA

, Volume 11, Issue 1, pp 74–123

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

  • Y. Martel
  • F. Merle

DOI: 10.1007/PL00001673

Cite this article as:
Martel, Y. & Merle, F. GAFA, Geom. funct. anal. (2001) 11: 74. doi:10.1007/PL00001673

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.

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