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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Published inCommunications in partial differential equations Vol. 46; no. 12; pp. 2325 - 2385
Main Authors Côte, Raphaël, Friederich, Xavier
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.12.2021
Taylor & Francis Ltd
Subjects
35B40 (primary)
Analysis of PDEs
Mathematical analysis
Mathematics
Multi-solitons
non-linear Schrödinger equations
Nonlinearity
Schrodinger equation
Smoothness
Solitary waves
Uniqueness
non-linear Schrödinger equations
smoothness
multi-solitons
uniqueness
Online AccessGet full text
ISSN0360-5302
1532-4133
DOI10.1080/03605302.2021.1941107

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Abstract 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.
AbstractList 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.
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.
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.
Author Friederich, Xavier
Côte, Raphaël
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10.1007/BF01221125
10.1016/j.anihpc.2006.01.001
10.1080/03605302.2010.503770
10.1103/RevModPhys.72.545
10.1017/fms.2014.13
10.1016/j.anihpc.2020.09.002
10.1007/s00205-017-1109-0
10.1112/plms/pds038
10.1512/iumj.2000.49.1893
10.1007/BF01403504
10.1016/j.matpur.2011.03.004
10.4171/RMI/592
10.1016/j.na.2010.05.045
10.1002/cpa.3160390103
10.1016/j.jde.2013.06.005
10.1353/ajm.2005.0033
10.1137/140960220
10.1016/S0021-7824(02)01274-6
10.1137/0516034
10.1007/BF02096981
10.1007/BF00275874
10.1017/S030821051500030X
10.1007/BF00251502
10.1088/0951-7715/27/11/2689
10.1007/BF00250555
10.1016/0022-1236(79)90076-4
10.1007/BF02787794
10.1016/j.cnsns.2014.06.028
10.1002/cpa.20292
10.4171/RMI/636
10.1016/0022-1236(90)90016-E
10.1090/tran/7303
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  doi: 10.1103/RevModPhys.72.545
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  doi: 10.1017/fms.2014.13
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  doi: 10.1016/j.anihpc.2020.09.002
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  doi: 10.1007/s00205-017-1109-0
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  start-page: rpn002
  issue: 4
  year: 2008
  ident: CIT0036
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  doi: 10.1112/plms/pds038
– ident: CIT0028
  doi: 10.1512/iumj.2000.49.1893
– ident: CIT0035
  doi: 10.1007/BF01403504
– volume-title: Bose-Einstein condensation
  year: 2003
  ident: CIT0002
– volume: 5
  start-page: 1408
  year: 1965
  ident: CIT0009
  publication-title: Sov. Math. J
– ident: CIT0020
  doi: 10.1016/j.matpur.2011.03.004
– ident: CIT0037
  doi: 10.4171/RMI/592
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  doi: 10.1016/j.na.2010.05.045
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  doi: 10.1016/j.jde.2013.06.005
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  doi: 10.1137/140960220
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  doi: 10.1016/S0021-7824(02)01274-6
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  doi: 10.1137/0516034
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  doi: 10.1007/BF02096981
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  doi: 10.1007/BF00275874
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  doi: 10.1017/S030821051500030X
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  doi: 10.1007/BF00251502
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  doi: 10.1088/0951-7715/27/11/2689
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  doi: 10.1007/BF00250555
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  doi: 10.1016/0022-1236(79)90076-4
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  doi: 10.1016/j.cnsns.2014.06.028
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  doi: 10.1002/cpa.20292
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  doi: 10.4171/RMI/636
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Snippet 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...
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...
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...
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SubjectTerms 35B40 (primary)
Analysis of PDEs
Mathematical analysis
Mathematics
Multi-solitons
non-linear Schrödinger equations
Nonlinearity
Schrodinger equation
Smoothness
Solitary waves
Uniqueness
Title On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations
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