Adiabatic Limit for Hyperbolic Ginzburg–Landau Equations
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.
KeywordsVortex Modulus Space Landau Equation Auxiliary System Dynamic Solution
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- 3.R. V. Palvelev, “Justification of adiabatic principle in Abelian Higgs model,” Proc. Moscow Math. Soc., 72, 281–314 (2011).Google Scholar