Quantum hydrodynamics, the quantum Benjamin-Ono equation, and the Calogero model

Collective field theory for the 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-the quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.