, Volume 11, Issue 1, pp 74-123

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

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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.

Submitted: December 1999, Revised version: January 2000, Final version: August 2000.