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Uspekhi Mat. Nauk, 2014, Volume 69, Issue 2(416), Pages 77–106 (Mi umn9574)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.4213/rm9574

Full text: PDF file (778 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2014, 69:2, 261–290

Bibliographic databases:

UDC: 517.95
MSC: 35Q55, 35Q53, 35B40, 35B44, 35B35
Received: 27.10.2013

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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\paper Near soliton dynamics and singularity formation for $L^2$ critical problems
\jour Uspekhi Mat. Nauk
\yr 2014
\vol 69
\issue 2(416)
\pages 77--106
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\jour Russian Math. Surveys
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\vol 69
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\pages 261--290
\crossref{https://doi.org/10.1070/RM2014v069n02ABEH004888}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Combet, Y. Martel, “Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation”, Bull. Sci. Math., 141:2 (2017), 20–103  crossref  mathscinet  zmath  isi  scopus
    2. J. Jendrej, “Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5”, J. Funct. Anal., 272:3 (2017), 866–917  crossref  mathscinet  zmath  isi  scopus
    3. J. Speck, “Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations”, Anal. PDE, 10:8 (2017), 2001–2030  crossref  mathscinet  zmath  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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