Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Title Scattering of Solitons for Schr\"odinger Equation Coupled to a
  Particle   We establish soliton-like asymptotics for finite energy solutions to the
Schr\"odinger equation coupled to a nonrelativistic classical particle. Any
solution with initial state close to the solitary manifold, converges to a sum
of traveling wave and outgoing free wave. The convergence holds in global
energy norm. The proof uses spectral theory and the symplectic projection onto
solitary manifold in the Hilbert phase space.

4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex