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.