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.
Cite
@article{arxiv.0810.5327,
title = {Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation},
author = {A. G. Abanov and E. Bettelheim and P. Wiegmann},
journal= {arXiv preprint arXiv:0810.5327},
year = {2009}
}
Comments
28 pages, 1 figure