, Volume 317, Issue 1, pp 69-97
Date: 13 Nov 2012

Multi-Vortex Non-radial Solutions to the Magnetic Ginzburg-Landau Equations

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Abstract

We show that there exists multi-vortex, non-radial, finite energy solutions to the magnetic Ginzburg-Landau equations on all of \({\mathbb{R}^2}\) . We use Lyapunov-Schmidt reduction to construct solutions which are invariant under rotations by \({\frac{2 \pi}{k}}\) (but not by rotations in O(2) in general) and reflections in the x− axis for some k ≥ 7.

Communicated by I. M. Sigal