  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.
