Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear amplification of coherent waves in media with soliton-type
  refractive index pattern   We derive the complex Ginzburg-Landau equation for the dynamical
self-diffraction of optical waves in a nonlinear cavity. The case of the
reflection geometry of wave interaction as well as a medium that possesses the
cubic nonlinearity (including a local and a nonlocal nonlinear responses) and
the relaxation is considered. A stable localized spatial structure in the form
of a "dark" dissipative soliton is formed in the cavity in the steady state.
The envelope of the intensity pattern, as well as of the dynamical grating
amplitude, takes the shape of a $\tanh$ function. The obtained complex
Ginzburg-Landau equation describes the dynamics of this envelope, at the same
time the evolution of this spatial structure changes the parameters of the
output waves. New effects are predicted in this system due to the
transformation of the dissipative soliton which takes place during the
interaction of a pulse with a continuous wave, such as: retention of the pulse
shape during the transmission of impulses in a long nonlinear cavity; giant
amplification of a seed pulse, which takes energy due to redistribution of the
pump continuous energy into the signal.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex