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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
67/2006

Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation

Andrew Komech, Scipio Cuccagna and Dmitry E. Pelinovsky

Abstract

We prove the instability of a "critical" solitary wave of the generalized Korteweg -- de Vries equation, the one with the speed at the border between the stability and instability regions. The instability mechanism involved is "purely nonlinear", in the sense that the linearization at a critical soliton does not have eigenvalues with positive real part. We prove that critical solitons correspond generally to the saddle-node bifurcation of two branches of solitons.

Received:
Jul 26, 2006
Published:
Jul 26, 2006

Related publications

inJournal
2007 Repository Open Access
Andrew Comech, Scipio Cuccagna and Dmitry E. Pelinovsky

Nonlinear instability of a critical traveling wave in the generalized Korteweg-de Vries equation

In: SIAM journal on mathematical analysis, 39 (2007) 1, pp. 1-33