Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay and scattering of solutions to nonlinear Schr\"odinger equations
  with regular potentials for nonlinearities of sharp growth   In this paper, we prove the decay and scattering in the energy space for
nonlinear Schr\"odinger equations with regular potentials in $\Bbb R^d$ namely,
$i{\partial _t}u + \Delta u - V(x)u + \lambda |u|^{p - 1}u = 0$. We will prove
decay estimate and scattering of the solution in the small data case when
$1+\frac{2}{d}<p\le1+\frac{4}{d-2}$, $d\ge3$. The index $1+\frac{2}{d}$ is
sharp for scattering concerning the result of W. Strauss [21].

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci