Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of Gross-Pitaevskii equations beyond the hydrodynamic
  approximation: Application to the vortex problem   We develop the multiscale technique to describe excitations of a
Bose-Einstein condensate (BEC) whose characteristic scales are comparable with
the healing length, thus going beyond the conventional hydrodynamical
approximation. As an application of the theory we derive approximate explicit
vortex and other solutions. The dynamical stability of the vortex is discussed
on the basis of the mathematical framework developed here, the result being
that its stability is granted at least up to times of the order of seconds,
which is the condensate lifetime. Our analytical results are confirmed by the
numerical simulations.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess