Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multisoliton solutions of the vector nonlinear Schr\"odinger equation
  (Kulish-Sklyanin model) and the vector mKdV equation   There exist two natural vector generalizations of the completely integrable
nonlinear Schr\"odinger (NLS) equation in $1+1$ dimensions: the well-known
Manakov model and the lesser-known Kulish-Sklyanin model. In this paper, we
propose a binary Darboux (or Zakharov-Shabat dressing) transformation that can
be directly applied to the Kulish-Sklyanin model. By deriving a simple closed
expression for iterations of the binary Darboux transformation, we obtain an
explicit formula for the $N$-soliton solution of the Kulish-Sklyanin model
under vanishing boundary conditions. Because the third-order symmetry of the
vector NLS equation can be reduced to a vector generalization of the modified
KdV (mKdV) equation, we can also obtain multisoliton (or multi-breather)
solutions of the vector mKdV equation in closed form.

17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con