Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Schr\"odinger Equation: Generalized Darboux Transformation and
  Rogue Wave Solutions   In this paper, we construct a generalized Darboux transformation for
nonlinear Schr\"odinger equation. The associated $N$-fold Darboux
transformation is given both in terms of a summation formula and in terms of
determinants. As applications, we obtain compact representations for the $N$-th
order rogue wave solutions of the focusing nonlinear Schr\"odinger equation and
Hirota equation. In particular, the dynamics of the general third order rogue
wave is discussed and shown to exhibit interesting structure.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg