Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large time behavior in nonlinear Schrodinger equation with time
  dependent potential   We consider the large time behavior of solutions to defocusing nonlinear
Schrodinger equation in the presence of a time dependent external potential.
The main assumption on the potential is that it grows at most quadratically in
space, uniformly with respect to the time variable. We show a general
exponential control of first order derivatives and momenta, which yields a
double exponential bound for higher Sobolev norms and momenta. On the other
hand, we show that if the potential is an isotropic harmonic potential with a
time dependent frequency which decays sufficiently fast, then Sobolev norms are
bounded, and momenta grow at most polynomially in time, because the potential
becomes negligible for large time: there is scattering, even though the
potential is unbounded in space for fixed time.

27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: econ