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Russian Mathematical Surveys, 2014, Volume 69, Issue 2, Pages 261–290
DOI: https://doi.org/10.1070/RM2014v069n02ABEH004888 (Mi rm9574) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Near soliton dynamics and singularity formation for $L^2$ critical problems

Y. Martela, F. Merlebc, P. Raphaelde, J. Szeftelfg

a Ècole Polytechnique, Centre de Mathématiques, Palaiseau, France
b Institut des Hautes Études Scientifiques, Bures-sur-Ivette, France
c Université de Cergy-Pontoise, Cergy-Pontoise, France
d Université Paul Sabatier, Toulouse
e Institut Universitaire de France, Paris
f Centre National de la Recherche Scientifique, Paris, France
g Ècole Normale Supérieure, Paris, France
English version PDF (737 kB) Citations (6)
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DOI: https://doi.org/10.1070/RM2014v069n02ABEH004888
Abstract: This survey reviews the state of the art concerning singularity formation for two canonical dispersive problems: the $L^2$ critical non-linear Schrödinger equation and the $L^2$ critical generalized KdV equation. In particular, the currently very topical question of classifying flows with initial data near a soliton is addressed.
Bibliography: 72 titles.
Keywords: non-linear Schrödinger equation, critical equation, generalized Korteweg–de Vries equation, blowup, soliton, blowup profile, qualitative behaviour of solutions, non-linear dispersive equation.
Received: 27.10.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2014, Volume 69, Issue 2(416), Pages 77–106
DOI: https://doi.org/10.4213/rm9574
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: 35Q55, 35Q53, 35B40, 35B44, 35B35
Language: English
Original paper language: Russian
Citation: Y. Martel, F. Merle, P. Raphael, J. Szeftel, “Near soliton dynamics and singularity formation for $L^2$ critical problems”, Uspekhi Mat. Nauk, 69:2(416) (2014), 77–106; Russian Math. Surveys, 69:2 (2014), 261–290
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:193
    English version PDF:31
    References:57
    First page:20
     
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