Particles versus fields in PT-symmetrically
deformed integrable systems
ANDREAS FRING
Centre for Mathematical Science,
E-mail: a.fring@city.ac.uk
Abstract. We
review some recent results on how ${\cal PT}$
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 Painlev\'{e}
test.
Keywords. Korteweg--de
Vries equation; Calogero--Moser--Sutherland
models; Painlev\'{e}
property; ${\cal PT}$ symmetry;
compactons.
PACS Nos 02.60.Lj; 02.30.Ik; 03.65.Ge; 03.50.-z; 11.30.Er