Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical simulation of knotted solutions for Maxwell equations   In this work, we use the finite differences in time domain (FDTD) numerical
method to compute and assess the validity of Hopf solutions, or hopfions, for
the electromagnetic field equations. In these solutions, field lines form
closed loops characterized by different knot topologies which are preserved
during their time evolution. Hopfions have been studied extensively in the past
from an analytical perspective but never, to the best of our knowledge, from a
numerical approach. The implementation and validation of this technique eases
the study of more complex cases of this phenomena; e.g. how these fields could
interact with materials (e.g. anisotropic or non-linear), their coupling with
other physical systems (e.g. plasmas), and also opens the path on their
artificial generation by different means (e.g. antenna arrays or lasers).

2
The categories of this paper are: math
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th