Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering-like phenomena of the periodic defocusing NLS equation   In this paper we prove approximation properties of the solutions of the
defoucsing NLS equation on the circle by nearly linear flows. In addition we
show that spatially periodic solutions of the defocusing NLS equation evolving
in fractional Sobolev spaces $H^s$ with $s\geq 1$ remain bounded for all times.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex