Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doubly Periodic Self-Dual Vortices for a Relativistic Non-Abelian
  Chern--Simons Model   In this paper we establish a multiplicity result concerning the existence of
doubly periodic solutions for a $2\times2$ nonlinear elliptic system arising in
the study of self-dual non-Abelian Chern--Simons vortices. We show that the
given system admits at least two solutions when the Chern--Simons coupling
parameter $\kappa>0$ is sufficiently small; while no solutions exist for
$\kappa>0$ sufficiently large. As in [36] we use a variational formulation of
the problem. Thus, we obtain a first solution via a (local) minimization method
and show that it is asymptotically gauge-equivalent to the (broken) principal
embedding vacuum of the system, as $\kappa\to 0$. Then we obtain the second
solution by a min-max procedure of "mountain pass" type.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn