Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Freezing of energy of a soliton in an external potential   In this paper we study the dynamics of a soliton in the generalized NLS with
a small external potential $\epsilon V$ of Schwartz class. We prove that there
exists an effective mechanical system describing the dynamics of the soliton
and that, for any positive integer $r$, the energy of such a mechanical system
is almost conserved up to times of order $\epsilon^{-r}$. In the rotational
invariant case we deduce that the true orbit of the soliton remains close to
the mechanical one up to times of order $\epsilon^{-r}$.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph