  We theoretically analyse a recent experiment reporting the observation of a
self-amplifying Hawking radiation in a flowing atomic condensate [J.Steinhauer,
Nature Physics, vol.10, pp.864, Nov 2014]. We are able to accurately reproduce
the experimental observations using a theoretical model based on the numerical
solution of a mean-field Gross-Pitaevskii equation that does not include
quantum fluctuations of the matter field. In addition to confirming the black
hole lasing mechanism, our results show that the underlying dynamical
instability has a classical hydrodynamic origin and is triggered by a seed of
deterministic nature, linked to the non-stationary of the process, rather than
by thermal or zero-point fluctuations.
