Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Are Maxwell knots integrable?   We review properties of the null-field solutions of source-free Maxwell
equations. We focus on the electric and magnetic field lines, especially on
limit cycles, which actually can be knotted and/or linked at every given
moment. We analyse the fact that the Poynting vector induces self-consistent
time evolution of these lines and demonstrate that the Abelian link invariant
is integral of motion. The same is expected to be true also for the non-Abelian
invariants (like Jones and HOMFLY-PT polynomials or Vassiliev invariants), and
many integrals of motion can imply that the Poynting evolution is actually
integrable. We also consider particular examples of the field lines for the
particular family of finite energy source-free "knot" solutions, attempting to
understand when the field lines are closed -- and can be discussed in terms of
knots and links. Based on computer simulations we conjecture that Ranada's
solution, where every pair of lines forms a Hopf link, is rather exceptional.
In general, only particular lines (a set of measure zero) are limit cycles and
represent closed lines forming knots/links, while all the rest are twisting
around them and remain unclosed. Still, conservation laws of Poynting evolution
and associated integrable structure should persist.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas