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https://www.ias.ac.in/article/fulltext/pram/073/02/0363-0373

Korteweg–de Vries equation; Calogero–Moser–Sutherland models; Painlevé property; $\mathcal{PT}$ symmetry; compactons.

We review some recent results on how $\mathcal{PT}$ 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 Painlevé test.

Andreas Fring¹

1. Centre for Mathematical Science, City University London, Northampton Square, London EC1V 0HB, UK

Published

August 2009