On the bifurcation theory of the Ginzburg–Landau equations

Nagy, Ákos; Oliveira, Gonçalo

doi:10.1090/proc/16510

On the bifurcation theory of the Ginzburg–Landau equations
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by Ákos Nagy and Gonçalo Oliveira;

Proc. Amer. Math. Soc. 152 (2024), 653-664

DOI: https://doi.org/10.1090/proc/16510

Published electronically: December 1, 2023

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Abstract:

We construct nonminimal and irreducible solutions to the Ginzburg–Landau equations on closed manifolds of arbitrary dimension with trivial first real cohomology. Our method uses bifurcation theory where the “bifurcation points” are characterized by the eigenvalues of a Laplace-type operator. To our knowledge these are the first such examples on nontrivial line bundles.

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