On the bifurcation theory of the Ginzburg–Landau equations
On the bifurcation theory of the Ginzburg–Landau equations
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.
15 pages, no figures, accepted version, comments are welcome! To appear in the Proceedings of the AMS. arXiv admin note: text overlap with arXiv:2103.05613
Bifurcations in context of PDEs, Mathematics - Differential Geometry, Ginzburg-Landau equations, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), FOS: Physical sciences, Bifurcation theory for PDEs on manifolds, Mathematical Physics (math-ph), 35Q56, 53C07, 58E15, 58J55, nonminimal solutions, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), bifurcation theory, Variational problems concerning extremal problems in several variables; Yang-Mills functionals, FOS: Mathematics, Mathematical Physics, Analysis of PDEs (math.AP)
Bifurcations in context of PDEs, Mathematics - Differential Geometry, Ginzburg-Landau equations, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), FOS: Physical sciences, Bifurcation theory for PDEs on manifolds, Mathematical Physics (math-ph), 35Q56, 53C07, 58E15, 58J55, nonminimal solutions, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), bifurcation theory, Variational problems concerning extremal problems in several variables; Yang-Mills functionals, FOS: Mathematics, Mathematical Physics, Analysis of PDEs (math.AP)
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