  Diffractive production is considered in the ultrahigh energy region where
pomeron exchange amplitudes are transformed into black disk ones due to
rescattering corrections. The corresponding corrections in hadron reactions
$h_1+h_3\to h_1+h_2+h_3$ with small momenta transferred ($q^2_{1\to 1}\sim
m^2/\ln^2s$, $q^2_{3\to 3}\sim m^2/\ln^2s$) are calculated in terms of the
$K$-matrix technique modified for ultrahigh energies. Small values of the
momenta transferred are crucial for introducing equations for amplitudes. The
three-body equation for hadron diffractive production reaction $h_1+h_3\to
h_1+h_2+h_3$ is written and solved precisely in the eikonal approach. In the
black disk regime final state scattering processes do not change the shapes of
amplitudes principally but dump amplitudes in a factor $\sim\frac 14$.
