  Propagation of ultrashort light pulses in disordered multilayers is studied
by using numerical simulations in time domain. We consider cases of
instantaneous and noninstantaneous Kerr nonlinearities of the structure
materials. The competitive nature of disorder and nonlinearity is revealed on
the long and short timescales. We also pay special attention to the effect of
pulse self-trapping in the photonic crystal with relaxing nonlinearity and show
the dependence of this effect on the level of disorder. We believe that the
results reported here will be useful not only in the field of optics but also
from the standpoint of the general problem of classical waves propagation in
nonlinear disordered periodic media.
