Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double resonant processes in $\chi^{(2)}$ nonlinear periodic media   In a one-dimensional periodic nonlinear $\chi^{(2)}$ medium, by choosing a
proper material and geometrical parameters of the structure, it is possible to
obtain two matching conditions for simultaneous generation of second and third
harmonics. This leads to new diversity of the processes of the resonant
three-wave interactions, which are discussed within the framework of slowly
varying envelope approach. In particular, we concentrate on the fractional
conversion of the frequency $\omega \to (2/3) \omega$. This phenomenon occurs
by means of intermediate energy transfer to the first harmonic at the frequency
$\omega/3$ and can be controlled by this mode. By analogy the same medium
allows "nondirect" second harmonic generation, controlled by the cubic
harmonic. Propagation of localized pulses in the form two coupled bright
solitons on first and third harmonics and a dark soliton on the second harmonic
is possible.

27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ