Pramana

, 73:363 | Cite as

Particles versus fields in \( \mathcal{P}\mathcal{T} \)-symmetrically deformed integrable systems

Article

Abstract

We review some recent results on how \( \mathcal{P}\mathcal{T} \) 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 nonlinear 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 Painlevé test.

Keywords

Korteweg-de Vries equation Calogero-Moser-Sutherland models Painlevé property \(\mathcal{P}\mathcal{T}\) symmetry compactons 

PACS Nos

02.60.Lj 02.30.Ik 03.65.Ge 03.50.-z 11.30.Er 

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Copyright information

© Indian Academy of Sciences 2009

Authors and Affiliations

  1. 1.Centre for Mathematical ScienceCity University LondonLondonUK

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