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Nonlinear PT−symmetric plaquettes
Li, K.; Kevrekidis, P.; Malomed, B.; Günther, U.;
Four basic two-dimensional (2D) plaquette configurations are introduced with onsite cubic nonlinearities, which may be used as building blocks for 2D PT-symmetric lattices. For each configuration, a dynamical model is developed and its PT symmetry is examined. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient. Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of direct simulations. In particular, stable localized modes are found in these systems, although the majority of identified solutions is unstable.
Keywords: PT quantum mechanics, PT oligomers, 2D plaquettes, 2D PT-symmetric lattices, nonlinear dynamics, bifurcations, stationary solutions, stability analysis, exceptional points


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Publ.-Id: 17589