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

Alexander G. Abanov, Eldad Bettelheim, Paul Wiegmann

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67 Scopus citations


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 analog of the 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 nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations.

Original languageAmerican English
Article number135201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number13
StatePublished - 2009


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