Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotic stability of solitons in the cubic NLS equation on the
  line   We use the inverse scattering transform, the auto-Backlund transformation and
the steepest descent method of Deift and Zhou to obtain the asymptotic
stability of the solitons in the cubic NLS (nonlinear Schrodinger) equation.

16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat