Nonlinear PT−symmetric plaquettes --- and beyond

Nonlinear 2-dimensional PT-symmetric plaquettes of various types are considered. A technique is developed to obtain explicit matrix representations for the parity (P) and for the time-reversal (T) operators starting from initially heuristically designed gain-loss setups of general 2D-type. The threshold behavior of the corresponding linear sub-systems is analyzed near PT-phase transition points in parameter space, the concrete type of exceptional point is established and the analytical construction of stationary solutions for the nonlinear setups is made explicit. The presentation is based on common work with Panayotis Kevrekidis, Kai Li and Boris Malomed [J. Phys. A 45, 444021 (2012)]. Next possible steps of technical extensions towards higher-dimensional soliton setups and required integrability tests via the search for Lax pairs of Zakharov-Shabat and Fordy-Kulish type are briefly sketched.