ON SMOOTHNESS AND UNIQUENESS OF MULTI-SOLITONS OF THE NON-LINEAR SCHRÖDINGER EQUATIONS

SUR LA REGULARITE ET L'UNICITE DES MULTI-SOLITONS DES EQUATIONS DE SCHRÖDINGER NON-LINEAIRES

Raphaël Côte (1) , Xavier Friederich (1)

1 IRMA - Institut de Recherche Mathématique Avancée

In this paper, we study some properties of multi-solitons for the non-linear Schrödinger equations in R^d with general non-linearities. Multi-solitons have already been constructed in H^1, successively by Merle, by Martel and Merle, and by Côte, Martel and Merle. We show here that multi-solitons are smooth, depending on the regularity of the non-linearity. We obtain also a result of uniqueness in some class, either when the ground states are all stable, or in the mass-critical case.

Mots clés: non-linear Schrödinger equations; multi-solitons; smoothness; uniqueness

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Côte, Xavier Friederich. ON SMOOTHNESS AND UNIQUENESS OF MULTI-SOLITONS OF THE NON-LINEAR SCHRÖDINGER EQUATIONS. 2020. ⟨hal-02873307v1⟩