Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New example of integrable nonlinear coupled equations with exact
  asymptotic singular solution in the context of laser-plasma interaction   A new set of nonlinear coupled equations is derived in the context of small
amplitude limit of the general wave equations in a fluid type warm
electrons/cold ions plasma irradiated by a continuous laser beam. This limit is
proved to be integrable by means of the spectral transform theory with singular
dispersion relation. An exact asymptotic solution is obtained. This model
accounts for a nonlinear mode coupling of the electrostatic waves with the ion
sound wave, and is shown to be unstable and does not propagate any stable small
amplitude solution. This instability is understood as a continuous secular
transfer of energy from the electrostatic wave to the ion sound wave through
the ponderomotive force. The exact mechanism of this transfer is exposed. The
dynamics of this energy transfer results in a singular asymptotic behavior of
the ion sound wave which explains the low penetration of the incident laser
beam.

6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci