The classical hydrodynamics of the Calogero-Sutherland model

TL;DR

This paper investigates the classical hydrodynamics of the Calogero-Sutherland model by mapping it onto the Benjamin-Ono equation, constructing soliton solutions, and analyzing the subtleties involved in the mapping process.

Contribution

It provides a detailed analysis of the classical hydrodynamics of the Calogero-Sutherland model and clarifies the mapping onto the Benjamin-Ono equation, including soliton solutions and correction subtleties.

Findings

Constructed soliton solutions for the hydrodynamic equations.

Identified subtleties in the mapping process involving singular sums and principal-part integrals.

Clarified the role of corrections in the classical hydrodynamics mapping.

Abstract

We explore the classical version of the mapping, due to Abanov and Wiegmann, of Calogero-Sutherland hydrodynamics onto the Benjamin-Ono equation ``on the double.'' We illustrate the mapping by constructing the soliton solutions to the hydrodynamic equations, and show how certain subtleties arise from the need to include corrections to the naive replacement of singular sums by principal-part integrals.