Justification of the adiabatic principle for hyperbolic Ginzburg-Landau equations
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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.
KeywordsModulus Space Gauge Transformation STEKLOV Institute Landau Equation Auxiliary System
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- 3.R. V. Pal’velev, “Justification of the Adiabatic Principle in the Abelian Higgs Model,” Tr. Mosk. Mat. Obshch. 72(2), 281–314 (2011) [Trans. Moscow Math. Soc. 2011, 219–244 (2011)].Google Scholar