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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 277, Pages 199–214 (Mi tm3392)  

This article is cited in 13 scientific papers (total in 13 papers)

Justification of the adiabatic principle for hyperbolic Ginzburg–Landau equations

R. V. Palvelev, A. G. Sergeev

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
References:
Abstract: We study the adiabatic limit in hyperbolic Ginzburg–Landau equations which are the Euler–Lagrange equations for the Abelian Higgs model. By passing to the adiabatic limit in these equations, we establish a correspondence between the solutions of the Ginzburg–Landau equations and adiabatic trajectories in the moduli space of static solutions, called vortices. Manton proposed a heuristic adiabatic principle stating that every solution of the Ginzburg–Landau equations with sufficiently small kinetic energy can be obtained as a perturbation of some adiabatic trajectory. A rigorous proof of this result has been found recently by the first author.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00178
11-01-12033-ofi-m
Ministry of Education and Science of the Russian Federation NSh-7675.2010.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work was supported in part by the Russian Foundation for Basic Research (project nos. 10-01-00178 and 11-01-12033-ofi-m-2011), by a grant of the President of the Russian Federation (project no. NSh-7675.2010.1), and by the scientific program "Nonlinear Dynamics" of the Presidium of the Russian Academy of Sciences.
Received in February 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 277, Pages 191–205
DOI: https://doi.org/10.1134/S0081543812040141
Bibliographic databases:
Document Type: Article
UDC: 514.763.43+514.83
Language: Russian
Citation: R. V. Palvelev, A. G. Sergeev, “Justification of the adiabatic principle for hyperbolic Ginzburg–Landau equations”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 199–214; Proc. Steklov Inst. Math., 277 (2012), 191–205
Citation in format AMSBIB
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\by R.~V.~Palvelev, A.~G.~Sergeev
\paper Justification of the adiabatic principle for hyperbolic Ginzburg--Landau equations
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 277
\pages 199--214
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
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\pages 191--205
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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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