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

Friederich, Xavier

doi:10.1016/j.anihpc.2020.11.010

Friederich, Xavier ¹

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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Résumé

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

Affiliations des auteurs :

Friederich, Xavier ¹

¹ Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg, Strasbourg, France

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     title = {Non dispersive solutions of the generalized {Korteweg-de} {Vries} equations are typically multi-solitons},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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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://archive.numdam.org/articles/10.1016/j.anihpc.2020.11.010/

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