Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cubic-quintic nonlinear Schr\"odinger equation with inverse-square
  potential   We consider the nonlinear Schr\"odinger equation in three space dimensions
with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in
the presence of an external inverse-square potential. We establish scattering
in the region of the mass-energy plane where the virial functional is
guaranteed to be positive. Our result parallels the scattering result of
\cite{R.Killip, T. Oh, O. Pocovnicu, and M. Visan} in the setting of the
standard cubic-quintic NLS.

8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat