Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On self-similar solutions of the vortex filament equation   We study self-similar solutions of the binormal curvature flow which governs
the evolution of vortex filaments and is equivalent to the Landau-Lifshitz
equation. The corresponding dynamics is described by the real solutions of
$\sigma$-Painlev\'{e} IV equation with two real parameters. Connection formulae
for Painlev\'{e} IV transcendents allow for a complete characterization of the
asymptotic properties of the curvature and torsion of the filament. We also
provide compact hypergeometric expressions for self-similar solutions
corresponding to corner initial conditions.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
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The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs