Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classical nonlinear Schr\"odinger model with a new integrable
  boundary   A new integrable boundary for the classical nonlinear Schr\"odinger model is
derived by dressing a boundary with a defect. A complete investigation of the
integrability of the new boundary is carried out in the sense that the boundary
${\cal K}$ matrix is derived and the integrability is proved via the classical
$r$-matrix. The issue of conserved charges is also discussed. The key point in
proving the integrability of the new boundary is the use of suitable modified
Poisson brackets. Finally, concerning the kind of defect used in the present
context, this investigation offers the opportunity to prove - beyond any doubts
- their integrability.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph