  Management of solitons in media with competing quadratic and cubic
nonlinearities is investigated. Two schemes, using rapid modulations of a
mismatch parameter, and of the Kerr nonlinearity parameter are studied. For
both cases, the averaged in time wave equations are derived. In the case of
mismatch management, the region of the parameters where stabilization is
possible is found. In the case of Kerr nonlinearity management, it is shown
that the effective $\chi^{(2)}$ nonlinearity depends on the intensity imbalance
between fundamental (FH) and second (SH) harmonics. Predictions obtained from
the averaged equations are confirmed by numerical simulations of the full
PDE's.
