# On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

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## Abstract

We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per fundamental cell. We also revisit the existence proof for the Abrikosov vortex lattices, streamlining some arguments and providing some essential details missing in earlier proofs for a single magnetic flux quantum per a fundamental cell.

## Keywords

Magnetic vortices Superconductivity Ginzburg-Landau equations Abrikosov vortex lattices Bifurcations## Mathematics Subject Classification (2010)

35Q56## Notes

### Acknowledgments

It is a pleasure to thank Max Lein for useful discussions and the anonymous referees for reading carefully the manuscript and many useful remarks and suggestions. The first author would like to thank Dmitri Chouchkov for useful discussions. The first and third authors’ research is supported in part by NSERC Grant No. NA7901. During the work on the paper, they enjoyed the support of the NCCR SwissMAP. The first author was also supported by the NSERC CGS program. The second author (P. S.) was partially supported by Fondo Basal CMM-Chile and Fondecyt postdoctoral grant 3160055.

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