Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610774 | Journal of Differential Equations | 2013 | 28 Pages |
Abstract
We study Ginzburg–Landau equations for a complex vector order parameter Ψ=(ψ+,ψ−)∈C2Ψ=(ψ+,ψ−)∈C2. We consider symmetric vortex solutions in the plane R2R2, ψ(x)=f±(r)ein±θψ(x)=f±(r)ein±θ, with given degrees n±∈Zn±∈Z, and prove the existence, uniqueness, and asymptotic behavior of solutions as r→∞r→∞. We also consider the monotonicity properties of solutions, and exhibit parameter ranges in which both vortex profiles f+f+, f−f− are monotone, as well as parameter regimes where one component is non-monotone. The qualitative results are obtained by means of a sub- and super-solution construction and a comparison theorem for elliptic systems.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Stan Alama, Qi Gao,