Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact exact solutions of the Gross-Pitaevskii equation for stable vortex
  modes   We construct exact solutions of the Gross-Pitaevskii equation for solitary
vortices, and approximate ones for fundamental solitons, in 2D models of
Bose-Einstein condensates with a spatially modulated nonlinearity of either
sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes
is determined by the discrete energy spectrum of a related linear
Schr\"{o}dinger equation. The VS families in the system with the attractive and
repulsive nonlinearity are mutually complementary. \emph{% Stable} VSs with
vorticity $S\geq 2$ and those corresponding to higher-order radial states are
reported for the first time, in the case of the attraction and repulsion,
respectively.

35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an