Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact static soliton solutions of 3+1 dimensional integrable theory with
  nonzero Hopf numbers   In this paper we construct explicitly an infinite number of Hopfions (static,
soliton solutions with non-zero Hopf topological charges) within the recently
proposed 3+1-dimensional, integrable and relativistically invariant field
theory. Two integers label the family of Hopfions we have found. Their product
is equal to the Hopf charge which provides a lower bound to the soliton's
finite energy. The Hopfions are constructed explicitly in terms of the toroidal
coordinates and shown to have a form of linked closed vortices.

22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess