Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable three-dimensional spinning optical solitons supported by
  competing quadratic and cubic nonlinearities   We show that the quadratic interaction of fundamental and second harmonics in
a bulk dispersive medium, combined with self-defocusing cubic nonlinearity,
give rise to completely localized spatiotemporal solitons (vortex tori) with
vorticity s=1. There is no threshold necessary for the existence of these
solitons. They are found to be stable against small perturbations if their
energy exceeds a certain critical value, so that the stability domain occupies
about 10% of the existence region of the solitons. We also demonstrate that the
s=1 solitons are stable against very strong perturbations initially added to
them. However, on the contrary to spatial vortex solitons in the same model,
the spatiotemporal solitons with s=2 are never stable.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
3
The categories of this paper are: physics