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Journal Articles Indiana University Mathematics Journal Year : 2012

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

Abstract

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.
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Dates and versions

hal-00747461 , version 1 (31-10-2012)

Identifiers

  • HAL Id : hal-00747461 , version 1

Cite

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⟩
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