NON DISPERSIVE SOLUTIONS OF THE GENERALIZED KDV EQUATIONS ARE TYPICALLY MULTI-SOLITONS

LES SOLUTIONS NON-DISPERSIVES DES EQUATIONS DE KDV GENERALISEES SONT TYPIQUEMENT DES MULTI-SOLITONS

Xavier Friederich (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense (in the spirit of [18]) 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.

Mots clés: generalized KdV equations; solitons; multi-solitons

Domaines: Equations aux dérivées partielles [math.AP]

Xavier Friederich. NON DISPERSIVE SOLUTIONS OF THE GENERALIZED KDV EQUATIONS ARE TYPICALLY MULTI-SOLITONS. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, In press, ⟨10.1016/j.anihpc.2020.11.010⟩. ⟨hal-02888404⟩