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

In this paper, we study some properties of multi-solitons for the non-linear Schrödinger equations in with general non-linearities. Multi-solitons have already been constructed in in papers by Merle (1990), Martel and Merle (2006), and Côte, Martel and Merle (2011). We show here that multi-solitons...

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Bibliographic Details
Published in:Communications in partial differential equations 2021-12, Vol.46 (12), p.2325-2385
Main Authors: Côte, Raphaël, Friederich, Xavier
Format: Article
Language:English
Subjects:
35B40 (primary)
Analysis of PDEs
Mathematical analysis
Mathematics
Multi-solitons
non-linear Schrödinger equations
Nonlinearity
Schrodinger equation
Smoothness
Solitary waves
Uniqueness
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Summary:In this paper, we study some properties of multi-solitons for the non-linear Schrödinger equations in with general non-linearities. Multi-solitons have already been constructed in in papers by Merle (1990), Martel and Merle (2006), and Côte, Martel and Merle (2011). 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.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2021.1941107