JournalsaihpcVol. 38, No. 5pp. 1525–1552

Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons

  • Xavier Friederich

    Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg, Strasbourg, France
Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons cover

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Abstract

We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense and which remain close to multi-solitons. We show that these solutions are necessarily pure multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization of multi-solitons and multi-breathers in terms of non dispersion.

Cite this article

Xavier Friederich, Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 5, pp. 1525–1552

DOI 10.1016/J.ANIHPC.2020.11.010