Andreas Fring
Articles written in Pramana – Journal of Physics
Volume 73 Issue 2 August 2009 pp 363-373
Particles versus fields in $\mathcal{PT}$-symmetrically deformed integrable systems
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.
Volume 74 Issue 6 June 2010 pp 857-865 Research Articles
We investigate whether the recently proposed $\mathcal{PT}$-symmetric extensions of generalized Korteweg–de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can be found. The Painlevé test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable.
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