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    • Particles versus fields in $\mathcal{PT}$-symmetrically deformed integrable systems

      Andreas Fring

      Volume 73 Issue 2 August 2009 pp 363-373

    • Fulltext

       

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

    • Keywords

       

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

    • Abstract

       

      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.

    • Author Affiliations

       

      Andreas Fring1

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

    • Dates

       
      Published
      August 2009

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