  Undoped and strongly photoexcited semiconductor superlattices with
field-dependent recombination behave as excitable or oscillatory media with
spatially discrete nonlinear convection and diffusion. Infinitely long,
dc-current-biased superlattices behaving as excitable media exhibit wave fronts
with increasing or decreasing profiles, whose velocities can be calculated by
means of asymptotic methods. These superlattices can also support pulses of the
electric field. Pulses moving downstream with the flux of electrons can be
constructed from their component wave fronts, whereas pulses advancing upstream
do so slowly and experience saltatory motion: they change slowly in long
intervals of time separated by fast transitions during which the pulses jump to
the previous superlattice period. Photoexcited superlattices can also behave as
oscillatory media and exhibit wave trains.
