Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nonintegrability of equations for long- and short-wave
  interactions   We examine the integrability of two models used for the interaction of long
and short waves in dispersive media. One is more classical but arguably cannot
be derived from the underlying water wave equations, while the other one was
recently derived. We use the method of Zakharov and Schulman to attempt to
construct conserved quantities for these systems at different orders in the
magnitude of the solutions. The coupled KdV-NLS model is shown to be
nonintegrable, due to the presence of fourth-order resonances. A coupled real
KdV - complex KdV system is shown to suffer the same fate, except for three
special choices of the coefficients, where higher-order calculations or a
different approach are necessary to conclude integrability or the absence
thereof.

6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: eess
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th