  The post-bounce oscillations of newly-born relativistic stars are expected to
lead to gravitational-wave emission through the excitation of nonradial
oscillation modes. At the same time, the star is oscillating in its radial
modes, with a central density variation that can reach several percent.
Nonlinear couplings between radial oscillations and polar nonradial modes lead
to the appearance of combination frequencies (sums and differences of the
linear mode frequencies). We study such combination frequencies using a
gauge-invariant perturbative formalism, which includes bilinear coupling terms
between different oscillation modes. For typical values of the energy stored in
each mode we find that gravitational waves emitted at combination frequencies
could become detectable in galactic core-collapse supernovae with advanced
interferometric or wide-band resonant detectors.
