  We study the fluxes emitted by black holes when using dispersive field
theories. We work with stationary one dimensional backgrounds which are
asymptotically flat on both sides of the horizon. The asymptotic fluxes are
governed by a 3x3 Bogoliubov transformation. The fluxes emitted by the
corresponding white holes are regular and governed by the inverse
transformation. We numerically compute the spectral properties of these fluxes
for both sub- and superluminal quartic dispersion. The leading deviations with
respect to the dispersionless flux are computed and shown to be governed by a
critical frequency above which there is no radiation. Unlike the UV scale
governing dispersion, its value critically depends on the asymptotic properties
of the background. We also study the flux outside the robust regime. In
particular we show that its low frequency part remains almost thermal but with
a temperature which significantly differs from the standard one. Application to
four dimensional black holes and Bose-Einstein condensates are in preparation.
