Journal of Mathematical Sciences

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

Adiabatic Limit for Hyperbolic Ginzburg–Landau Equations

  • Armen Glebovich Sergeev


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.


Vortex Modulus Space Landau Equation Auxiliary System Dynamic Solution 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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