Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and instability of standing waves for a generalized Choquard
  equation with potential   We are going to study the standing waves for a generalized Choquard equation
with potential: $$ -i\partial_t u-\Delta
u+V(x)u=(|x|^{-\mu}\ast|u|^p)|u|^{p-2}u, \ \ \hbox{in}\ \
\mathbb{R}\times\mathbb{R}^3, $$ where $V(x)$ is a real function, $0<\mu<3$,
$2-\mu/3<p<6-\mu$ and $\ast$ stands for convolution. Under suitable assumptions
on the potential and appropriate frequency $\omega$ , the stability and
instability of the standing waves $u=e^{i \omega t}\varphi(x)$ are investigated .

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn