Particles versus fields in PT-symmetrically deformed integrable systems

TL;DR

This paper explores how PT-symmetry can generate new integrable models, including complex multi-particle systems and deformed field equations, with some exhibiting unique solutions like compactons.

Contribution

It introduces novel PT-symmetric deformations of integrable systems, connecting multi-particle models with non-linear field equations and analyzing their integrability.

Findings

PT-symmetry enables construction of new integrable models

Deformed Calogero-Moser-Sutherland models arise from field equations

Some deformed equations admit compacton solutions

Abstract

We review some recent results on how PT-symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the Calogero-Moser-Sutherland models, are shown to arise naturally from real valued field equations of non-linear integrable systems. Deformations of complex non-linear integrable field equations, some of them even allowing for compacton solutions, are also investigated. The integrabilty of various systems is established by means of the Painleve test