Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering for a Nonlinear Schr\"odinger Equation with a Potential   We consider a 3d cubic focusing nonlinear Schr\"odinger equation with a
potential $$i\partial_t u+\Delta u-Vu+|u|^2u=0,$$ where $V$ is a real-valued
short-range potential having a small negative part. We find criteria for global
well-posedness analogous to the homogeneous case $V=0$
(Duyckaerts-Holmer-Roudenko). Moreover, by the concentration-compactness
approach, we prove that if $V$ is repulsive, such global solutions scatter.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg