  For the superconducting phase with a d-wave order parameter and zero
temperature the magnetic susceptibility of the t-J model is calculated using
the Mori projection operator technique. Conditions for the appearance of an
incommensurate magnetic response below the resonance frequency are identified.
A fast decay of the tails of the hole coherent peaks and a weak intensity of
the hole incoherent continuum near the Fermi level are enough to produce an
incommensurate response using different hole dispersions established for
$p$-type cuprates, in which such response was observed. In this case, the
nesting of the itinerant-electron theory or the charge modulation of the stripe
theory is unnecessary for the incommensurability. The theory reproduces the
hourglass dispersion of the susceptibility maxima with their location in the
momentum space similar to that observed experimentally. The upper branch of the
dispersion stems from the excitations of localized spins, while the lower one
is due to the incommensurate maxima of their damping. The narrow and intensive
resonance peak arises if the frequency of these excitations at the
antiferromagnetic momentum lies below the edge of the two-fermion continuum;
otherwise the maximum is broad and less intensive.
