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Journal of Mathematical Sciences

, Volume 202, Issue 6, pp 887–896 | Cite as

Adiabatic Limit for Hyperbolic Ginzburg–Landau Equations

  • Armen Glebovich Sergeev
Article

Abstract

We study the adiabatic limit in hyperbolic Ginzburg–Landau equations which are Euler–Lagrange equations for the Abelian Higgs model. Solutions of Ginzburg–Landau equations in this limit converge to geodesics on the moduli space of static solutions in the metric determined by the kinetic energy of the system. According to heuristic adiabatic principle, every solution of Ginzburg–Landau equations with sufficiently small kinetic energy can be obtained as a perturbation of some geodesic. A rigorous proof of this result was proposed recently by Palvelev.

Keywords

Vortex Modulus Space Landau Equation Auxiliary System Dynamic Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    R. V. Palvelev, “Justification of adiabatic principle in Abelian Higgs model,” Proc. Moscow Math. Soc., 72, 281–314 (2011).Google Scholar
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    D. Stuart, “Dynamics of Abelian Higgs vortices in the near Bogomolny regime,” Commun. Math. Phys., 159, 51–91 (1994).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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