  We report the results of Monte Carlo simulation of electron dynamics in
stationary and space- and time-dependent electric fields in compensated GaN
samples. We have determined the frequency and wavevector dependencies of the
dynamic conductivity, $\sigma_{\omega,q}$. We have found that the spatially
dependent dynamic conductivity of the drifting electrons can be negative under
stationary electric fields of moderate amplitudes, $2..5$ kV/cm. This effect is
realized in a set of frequency windows. The low-frequency window with negative
dynamic conductivity is due to the Cherenkov mechanism. For this case the
time-dependent field induces a {\it traveling wave} of the electron
concentration in real space and a {\it standing wave} in the energy/momentum
space. The higher frequency windows of negative dynamic conductivity are
associated with the optical phonon transient time resonances. For this case the
time-dependent field is accompanied by oscillations of the electron
distribution in the form of the {\it traveling} waves in both the real space
and the energy/momentum space. We discuss the optimal conditions for the
observation of these effects. We suggest that the studied negative dynamic
conductivity can be used to amplify electromagnetic waves at the expense of
energy of the stationary field and current.
