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In the present work we focus on the cases of two-site (dimer) and three-site(trimer) configurations, i.e. oligomers, respecting the parity-time (PT)symmetry, i.e., with a spatially odd gain-loss profile. We examine differenttypes of solutions of such configurations with linear and nonlinear gain/lossprofiles. Solutions beyond the linear PT-symmetry critical point as well assolutions with asymmetric linearization eigenvalues are found in both thenonlinear dimer and trimer. The latter feature is absent in linear PT-symmetrictrimers, while both of them are absent in linear PT symmetric dimers.Furthermore, nonlinear gain/loss terms enable the existence of both symmetricand asymmetric solution profiles (and of bifurcations between them), while onlysymmetric solutions are present in the linear PT-symmetric dimers and trimers.The linear stability analysis around the obtained solutions is discussed andtheir dynamical evolution is explored by means of direct numerical simulations.Finally, a brief discussion is also given of recent progress in the context ofPT-symmetric quadrimers.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis