Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons
Friederich, Xavier1
1 Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg, Strasbourg, France
Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1525-1552.
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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.

DOI : 10.1016/j.anihpc.2020.11.010
Classification : 35B53, 35Q53, 35B40, 35B65
Mots-clés : Generalized KdV equations, Solitons, Multi-solitons
Friederich, Xavier 1

1 Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg, Strasbourg, France 
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Friederich, Xavier. Non dispersive solutions of the generalized Korteweg-de Vries equations are typically multi-solitons. Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1525-1552. doi : 10.1016/j.anihpc.2020.11.010. http://www.numdam.org/articles/10.1016/j.anihpc.2020.11.010/

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