  The production of Hawking radiation by a single horizon is not dependent on
the high-frequency dispersion relation of the radiated field. When there are
two horizons, however, Corley and Jacobson have shown that superluminal
dispersion leads to an amplification of the particle production in the case of
bosons. The analytic theory of this "black hole laser" process is quite
complicated, so we provide some numerical results in the hope of aiding
understanding of this interesting phenomenon. Specifically, we consider sonic
horizons in a moving fluid. The theory of elementary excitations in a
Bose-Einstein condensate provides an example of "superluminal" (Bogoliubov)
dispersion, so we add Bogoliubov dispersion to Unruh's equation for sound in
the fluid. A white-hole/black-hole horizon pair will then display black hole
lasing. Numerical analysis of the evolution of a wave packet gives a clear
picture of the amplification process. By utilizing the similarity of a
radiating horizon to a parametric amplifier in quantum optics we also analyze
the black hole laser as a quantum-optical network.
