Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Three-Wave Resonant Interaction: Deformation of the Plane-Wave
  Solutions and Darboux Transformations   The plane wave solutions of the three-wave resonant interaction in the plane
are considered. It is shown that rank-one constraints over the right
derivatives of invertible operators on an arbitrary linear space gives
solutions of the three-wave resonant interaction that can be understood as a
Darboux transformation of the plane wave solutions. The method is extended
further to obtain general Darboux transformations: for any solution of the
three-wave interaction problem and vector solutions of the corresponding Lax
pair large families of new solutions, expressed in terms of Grammian type
determinants of these vector solutions, are given.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph