Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonminimal solutions to the Ginzburg-Landau equations   We use two different methods to prove the existence of novel, nonminimal and
irreducible solutions to the Ginzburg-Landau equations on closed manifolds. To
our knowledge these are the first such examples on nontrivial line bundles,
that is, with nonzero total magnetic flux. The first method works with the
2-dimensional, critically coupled Ginzburg-Landau theory and uses the topology
of the moduli space. This method is nonconstructive, but works for all values
of the remaining coupling constant. We also prove the instability of these
solutions. The second method uses bifurcation theory to construct solutions,
and is applicable in higher dimensions and for noncritical couplings, but only
when the remaining coupling constant is close to the "bifurcation points",
which are characterized by the eigenvalues of a Laplace-type operator.

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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con