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

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 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.
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https://hal.archives-ouvertes.fr/hal-02873307
Contributor : Xavier Friederich <>
Submitted on : Tuesday, June 23, 2020 - 9:18:47 AM
Last modification on : Monday, July 6, 2020 - 11:49:13 AM

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  • HAL Id : hal-02873307, version 2
  • ARXIV : 2006.10987

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Raphaël Côte, Xavier Friederich. ON SMOOTHNESS AND UNIQUENESS OF MULTI-SOLITONS OF THE NON-LINEAR SCHRÖDINGER EQUATIONS. 2020. ⟨hal-02873307v2⟩

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