Skip to main content
SpringerLink
Log in

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

  • Published:
Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Département de Mathématiques, Université de Cergy—Pontoise, 2 avenue Adolphe Chauvin, BP 222, 95302 Cergy—Pontoise, France, , , , , , FR

    Y. Martel

  2. Département de Mathématiques, Université de Cergy—Pontoise, 2 avenue Adolphe Chauvin, BP 222, 95302 Cergy—Pontoise, France, and Institut Universitaire de France, , , , , , FR

    F. Merle

Authors
  1. Y. Martel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Merle
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martel, Y., Merle, F. Instability of solitons for the critical generalized Korteweg—de Vries equation . GAFA, Geom. funct. anal. 11, 74–123 (2001). https://doi.org/10.1007/PL00001673

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/PL00001673

Keywords

Search

Navigation