Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of overlapping vortices in complex scalar fields   We investigate dynamics of overlapping vortices in the nonlinear
Schr\"{o}dinger equation, the nonlinear heat equation and in the equation with
an intermediate Schr\"{o}dinger-diffusion dynamics. Because of formal
similarity on a perturbative level we discuss also the nonlinear wave equation
(Goldstone model). Special solutions are found like vortex helices,
double-helices and braids, breather states and vortex mouths. A pair of
vortices in the Goldstone model scatters by the right angle in the head-on
collision. It is found that in a dissipative system there is a characteristic
lenght scale above which vortices can be entangled but below which the
entanglement is unstable.

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The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat