  In a recent MIT experiment, a new form of superradiant Rayleigh scattering
was observed in Bose-Einstein condensates. We present a detailed theory of this
phenomena in which the directional dependence of the scattering rate and
condensate depletion lead to mode competition which is ultimately responsible
for superradiance. The nonlinear response of the system is highly sensitive to
initial quantum fluctuations which cause large run to run variations in the
observed superradiant pulses.
