2008/10/29 by A. G. Abanov, E. Bettelheim, P. Wiegmann · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.str-el #cond-mat.mes-hall #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8113/42/13/135201
published as J.Phys.A42:135201,2009 · 28 pages, 1 figure
arxiv created 2008/10/29 · arxiv updated 2009/12/01
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.