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Symmetric vortices for two-component Ginzburg-Landau systems
We study Ginzburg--Landau equations for a complex vector order parameter
Psi=(psi_+,psi_-). We consider symmetric (equivariant) vortex solutions in the
plane R^2 with given degrees n_\pm, and prove existence, uniqueness, and
asymptotic behavior of solutions for large r. We also consider the monotonicity
properties of solutions, and exhibit parameter ranges in which both vortex
profiles |psi_+|, |psi_i| are monotone, as well as parameter regimes where one
component is non-monotone. The qualitative results are obtained by means of a
sub- and supersolution construction and a comparison theorem for elliptic
systems.Comment: 32 page
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