Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knotted optical vortex lines in nonlinear saturable medium   In last 50 years, a significant progress was noticed in medicine,
communications and entertainment. Such advanced development of these fields was
directly related to ability of controlling light. Photonics is exactly about
this ability. At the present time, photonics is walking together with a
fundamental physical concept, optical soliton. Optical solitons are
shape-preserving laser beams. They are found potentially useful in data
transmission, which is very significant nowadays. Hence, research in the field
of optical solitons is still a vital issue. When optical soliton is perturbed
in a specific manner, there appear zeros of optical field around the soliton,
which are called optical vortices. In general optical vortices are lines in
space. Hence, we might expect them to become knotted. Knotting optical vortices
around perturbed seems spontaneous and cannot be directly predicted. To explain
this phenomenon, a similar system is constructed based on perturbation theory.
In this system, however, we have a mathematical problem which yet lacks a full
understanding. We address this problem by introducing concepts from three
disciplines: laser physics, knot theory and singular optics. We believe that
understanding the mechanism underlying spontaneous knotting of optical vortices
will be a step forward in other systems too, such as quantum turbulence in
superfluids and formation of optical vortices around other types of optical
solitons.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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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: q-fin
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph