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

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

2008-10-29

arxiv.org/abs/0810.5327v1

J.Phys.A42:135201,2009

Physics

Condensed Matter

Strongly Correlated Electrons

28 pages, 1 figure

Scientific paper

10.1088/1751-8113/42/13/135201

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.

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