Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering for the focusing $L^{2}$ -supercritical and $\dot
  H^2$-subcritical biharmonic NLS Equations   We consider the focusing $\dot H^{s_c}$-critical biharmonic Schr\"odinger
equation, and prove a global wellposedness and scattering result for the radial
data $u_0\in H^2(\mathbb R^N)$ satisfying $
M(u_0)^{\frac{2-s_c}{s_c}}E(u_0)<M(Q)^{\frac{2-s_c}{s_c}}E(Q) $ and $
\|u_{0}\|^{\frac{2-s_c}{s_c}}_{2}\|\Delta
u_{0}\|_{2}<\|Q\|^{\frac{2-s_c}{s_c}}_{2}\|\Delta Q\|_{2}, $ where
$s_c\in(0,2)$ and $Q$ is the ground state of $\Delta^2Q+(2-s_c)Q-|Q|^{p-1}Q=0$.

30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph