  Collective field theory for Calogero model represents particles with
fractional statistics in terms of hydrodynamic modes -- density and velocity
fields. We show that the quantum hydrodynamics of this model can be written as
a single evolution equation on a real holomorphic Bose field -- quantum
integrable Benjamin-Ono equation. It renders tools of integrable systems to
studies of nonlinear dynamics of 1D quantum liquids.
