Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On fractional Schrodinger systems of Choquard type   In this article, we first employ the concentration compactness techniques to
prove existence and stability results of standing waves for nonlinear
fractional Schr\"{o}dinger-Choquard equation \[ i\partial_t\Psi +
(-\Delta)^{\alpha}\Psi = a |\Psi|^{s-2}\Psi+\lambda \left(
\frac{1}{|x|^{N-\beta}} \star |\Psi|^p \right)|\Psi|^{p-2}\Psi\ \ \
\mathrm{in}\ \mathbb{R}^{N+1}, \] where $N\geq 2$, $\alpha\in (0,1)$, $\beta\in
(0, N)$, $s\in (2, 2+\frac{4\alpha}{N})$, $p\in [2,
1+\frac{2\alpha+\beta}{N})$, and the constants $a, \lambda$ are nonnegative
satisfying $a+\lambda > 0.$ We then extend the arguments to establish similar
results for coupled standing waves of nonlinear fractional Schr\"{o}dinger
systems of Choquard type. The same argument works for equations with an
arbitrary number of combined nonlinearities and when $|x|^{\beta-N}$ is
replaced by a more general convolution potential $\mathcal{K}:\mathbb{R}^N\to
[0, \infty)$ under certain assumptions. The same arguments can be applied and
the results are identical for the case $\alpha=1$ as well.

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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess