Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Static Hopfions in the extended Skyrme-Faddeev model   We construct static soliton solutions with non-zero Hopf topological charges
to a theory which is an extension of the Skyrme-Faddeev model by the addition
of a further quartic term in derivatives. We use an axially symmetric ansatz
based on toroidal coordinates, and solve the resulting two coupled non-linear
partial differential equations in two variables by a successive over-relaxation
(SOR) method. We construct numerical solutions with Hopf charge up to four, and
calculate their analytical behavior in some limiting cases. The solutions
present an interesting behavior under the changes of a special combination of
the coupling constants of the quartic terms. Their energies and sizes tend to
zero as that combination approaches a particular special value. We calculate
the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and
find that it vanishes at that same special value of the coupling constants. In
addition, the model presents an integrable sector with an infinite number of
local conserved currents which apparently are not related to symmetries of the
action. In the intersection of those two special sectors the theory possesses
exact vortex solutions (static and time dependent) which were constructed in a
previous paper by one of the authors. It is believed that such model describes
some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and
our results may be important in identifying important structures in that strong
coupling regime.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph