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.References
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Bibliographic Information
- Ákos Nagy
- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 076389
- ORCID: 0000-0002-1799-7631
- Email: contact@akosnagy.com
- Gonçalo Oliveira
- Affiliation: Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
- MR Author ID: 1087767
- ORCID: 0000-0002-4990-1788
- Email: goncalo.m.f.oliveira@tecnico.ulisboa.pt
- Received by editor(s): October 10, 2022
- Received by editor(s) in revised form: April 4, 2023, and April 6, 2023
- Published electronically: December 1, 2023
- Additional Notes: The second author was supported by Fundação Serrapilheira 1812-27395, by CNPq grants 428959/2018-0 and 307475/2018-2, and FAPERJ through the program Jovem Cientista do Nosso Estado E-26/202.793/2019.
- Communicated by: Lu Wang
- © Copyright 2023 by the authors
- Journal: Proc. Amer. Math. Soc. 152 (2024), 653-664
- MSC (2020): Primary 35Q56, 53C07, 58E15, 58J55
- DOI: https://doi.org/10.1090/proc/16510
- MathSciNet review: 4683847