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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 277, Pages 199–214
(Mi tm3392)
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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
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.
Received in February 2012
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
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https://www.mathnet.ru/eng/tm3392 https://www.mathnet.ru/eng/tm/v277/p199
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Abstract page: | 397 | Full-text PDF : | 70 | References: | 67 |
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