1. Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation.
- Author
-
Alexander G Abanov, Eldad Bettelheim, and Paul Wiegmann
- Subjects
HYDRODYNAMICS ,BENJAMIN-Ono equations ,QUANTUM theory ,MATHEMATICAL models ,CHIRALITY of nuclear particles ,PARTIAL differential equations ,MATHEMATICAL physics - 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 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. [ABSTRACT FROM AUTHOR]
- Published
- 2009