Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki
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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2002, Volume 75, Issue 7, Pages 428–1 (Mi jetpl3078)  
This article is cited in 1 scientific paper (total in 1 paper)

METHODS OF THEORETICAL PHYSICS

Collapse in the nonlinear Schrödinger equation of critical dimension $\{\mathbf{\sigma =1,\,D=2} \}$

Yu. N. Ovchinnikovab, I. M. Sigalc

a Max Planck Institute for the Physics of Complex Systems
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Department of Mathematics, University of Toronto
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Abstract: Collapsing solutions to the nonlinear Schrödinger equation of critical dimension $\{\sigma =1,\,D=2 \}$ are analyzed in the adiabatic approximation. A three-parameter set of solutions is obtained for the scale factor $\lambda(t)$. It is shown that the Talanov solution lies on the separatrix between the regions of collapse and convenient expansion. A comparison with numerical solutions indicates that weakly collapsing solutions provide a good initial approximation to the collapse problem.
Received: 27.02.2002
English version:
Journal of Experimental and Theoretical Physics Letters, 2002, Volume 75, Issue 7, Pages 357–361
DOI: https://doi.org/10.1134/1.1485267
Bibliographic databases:
Document Type: Article
PACS: 02.30.Jr, 03.65.Ge
Language: Russian
Citation: Yu. N. Ovchinnikov, I. M. Sigal, “Collapse in the nonlinear Schrödinger equation of critical dimension $\{\mathbf{\sigma =1,\,D=2} \}$”, Pis'ma v Zh. Èksper. Teoret. Fiz., 75:7 (2002), 428–1; JETP Letters, 75:7 (2002), 357–361
Citation in format AMSBIB
\Bibitem{OvcSig02}
\by Yu.~N.~Ovchinnikov, I.~M.~Sigal
\paper Collapse in the nonlinear Schr\"odinger equation of critical dimension $\{\mathbf{\sigma =1,\,D=2} \}$
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2002
\vol 75
\issue 7
\pages 428--1
\mathnet{http://mi.mathnet.ru/jetpl3078}
\transl
\jour JETP Letters
\yr 2002
\vol 75
\issue 7
\pages 357--361
\crossref{https://doi.org/10.1134/1.1485267}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0040668158}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Письма в Журнал экспериментальной и теоретической физики Pis'ma v Zhurnal Иksperimental'noi i Teoreticheskoi Fiziki
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