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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.

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Correspondence to F. Ting.

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Communicated by I. M. Sigal

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Ting, F., Wei, J. Multi-Vortex Non-radial Solutions to the Magnetic Ginzburg-Landau Equations. Commun. Math. Phys. 317, 69–97 (2013). https://doi.org/10.1007/s00220-012-1612-y

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