Solitons in the Calogero-Sutherland Collective-Field Model

TL;DR

This paper finds static and moving soliton solutions in the Calogero-Sutherland collective-field model, revealing different types of excitations depending on the statistical parameter, with implications for understanding collective behaviors.

Contribution

It introduces explicit soliton solutions in the model's Bogomol'nyi limit, highlighting new static and dynamic phenomena related to the statistical parameter.

Findings

Static solitons in the Bogomol'nyi limit

Moving solitons with no static limit for λ>1

Solitons represent holes and lumps depending on λ

Abstract

In the Bogomol'nyi limit of the Calogero-Sutherland collective-field model we find static-soliton solutions. The solutions of the equations of motion are moving solitons, having no static limit for $\l>1$. They describe holes and lumps, depending on the value of the statistical parametar $\l$.