On compound vortices in a two-component Ginzburg-Landau functional

Stan Alama (1) , Lia Bronsard (1) , Petru Mironescu (2)

1 Department of Mathematics and Statistics [Hamilton]
2 EDPA - Équations aux dérivées partielles, analyse

We study the structure of vortex solutions in a Ginzburg-Landau system for two complex valued order parameters. We consider the Dirichlet problem in the unit disk in ${\mathbb R}^2$ with symmetric, degree-one boundary condition, as well as the associated degree-one entire solutions in all of ${\mathbb R}^2$. Each problem has degree-one equivariant solutions with radially symmetric profile vanishing at the origin, of the same form as the unique (complex scalar) Ginzburg-Landau minimizer. We find that there is a range of parameters for which these equivariant solutions are the unique locally energy minimizing solutions for the coupled system. Surprisingly, there is also a parameter regime in which the equivariant solutions are unstable, and minimizers must vanish separately in each component of the order parameter.

Mots clés: symmetry breaking; Ginzburg-Landau

Domaines: Equations aux dérivées partielles [math.AP]

Stan Alama, Lia Bronsard, Petru Mironescu. On compound vortices in a two-component Ginzburg-Landau functional. Indiana University Mathematics Journal, 2012, 61 (5), pp.1861--1909. ⟨hal-00747461⟩