title: Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis.
abstract: 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 different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT-symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear PT-symmetric trimers, while both of them are absent in linear PT-symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear PT-symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of PT-symmetric quadrimers.
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA.
authors.forename: M
authors.initials: M
authors.lastname: Duanmu
authors.forename: K
authors.initials: K
authors.lastname: Li
authors.forename: R L
authors.initials: RL
authors.lastname: Horne
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: N
authors.initials: N
authors.lastname: Whitaker