Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy scattering for a class of inhomogeneous nonlinear Schr\"odinger
  equation in two dimensions   We consider a class of $L^2$-supercritical inhomogeneous nonlinear
Schr\"odinger equations in two dimensions
  \[
  i\partial_t u + \Delta u = \pm |x|^{-b} |u|^\alpha u, \quad (t,x) \in
\mathbb{R} \times \mathbb{R}^2,
  \]
  where $0<b<1$ and $\alpha>2-b$. By adapting a new approach of
Arora-Dodson-Murphy \cite{ADM}, we show the energy scattering for the equation
with radially symmetric initial data. In the focusing case, our result extends
the one of Farah-Guzm\'an \cite{FG-high} to the whole range of $b$ where the
local well-posedness is available. In the defocusing case, our result extends
the one in \cite{Dinh-scat} where the energy scattering for non-radial initial
data was established in dimensions $N\geq 3$.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin