Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable knots in the trapped Bose-Einstein condensates   The knot of spin texture is studied within the two-component Bose-Einstein
condensates which are described by the nonlinear Gross-Pitaevskii equations. We
start from the non-interacting equations including an axisymmetric harmonic
trap to obtain an exact solution, which exhibits a non-trivial topological
structure. The spin-texture is a knot with an integral Hopf invariant. The
stability of the knot is verified by numerically evolving the nonlinear
Gross-Pitaevskii equations along imaginary time.

6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio