  Using a 3D Finite-Difference Time-Domain parallel code, we report on the
linear and nonlinear propagation of light pulses in a disordered assembly of
scatterers, whose spatial distribution is generated by a Molecular Dynamics
code; refractive index dispersion is also taken into account. We calculate the
static and dynamical diffusion constant of light, while considering a pulsed
excitation. Our results are in quantitative agreement with reported
experiments, also furnishing evidence of a non-exponential decay of the
transmitted pulse in the linear regime and in the presence of localized modes.
By using an high power excitation, we numerically demonstrate the
``modulational instability random laser'': at high peak input powers energy is
transferred to localized states from the input pulse, via third-order
nonlinearity and optical parametric amplification, and this process is signed
by a power-dependent non-exponential time-decay of the transmitted pulse.
