  If the dark matter in the universe is a self-gravitating Bose-Einstein
condensate (BEC) with quartic self-interaction described by the
Gross-Pitaevskii-Poisson system, the adhesion model, the Burgers equation and
the cosmological Kardar-Parisi-Zhang (KPZ) equation that have been introduced
heuristically to solve the problems inherent to cold dark matter (CDM) models
find a natural justification and an interesting generalization.
