Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetries for exact solutions to the nonlinear Schr\"odinger equation   A certain symmetry is exploited in expressing exact solutions to the focusing
nonlinear Schr\"odinger equation in terms of a triplet of constant matrices.
Consequently, for any number of bound states with any number of multiplicities
the corresponding soliton solutions are explicitly written in a compact form in
terms of a matrix triplet. Conversely, from such a soliton solution the
corresponding transmission coefficients, bound-state poles, bound-state norming
constants and Jost solutions for the associated Zakharov-Shabat system are
evaluated explicitly. It is also shown that these results hold for the matrix
nonlinear Schr\"odinger equation of any matrix size.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio