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arXiv · 2006.10987

On smoothness and uniqueness of multi-solitons of the non-linear Schr{\"o}dinger equations

Raphaël Côte·Xavier Friederich
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Abstract

In this paper, we study some properties of multi-solitons for the non-linear Schr{\"o}dinger 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 C{\^o}te, 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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Raphaël Côte, Xavier Friederich. 2020-06-19. On smoothness and uniqueness of multi-solitons of the non-linear Schr{\"o}dinger equations. https://arxiv.org/abs/2006.10987

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