On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations

Sur la régularité et l'unicité des multi-solitons des équations de Schrödinger non-linéaires

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

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Côte, Xavier Friederich. On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations. Communications in Partial Differential Equations, In press, ⟨10.1080/03605302.2021.1941107⟩. ⟨hal-02873307v3⟩