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

2020/06/19 by Côte, Raphaël, Friederich, Xavier · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.10987

Abstract

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 H¹, 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.

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