Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation

Abstract

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analogue of Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the Chiral Non-linear Equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the Chiral Non-Linear Equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the Chiral Non-Linear equations.

28 pages, 1 figure

References in corpus (5)

• Collective fields, Calogero-Sutherland model and generalized matrix models
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Solitons in the Calogero-Sutherland Collective-Field Model

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