
Article
PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics
Physical Review E
(2011)
Abstract
In the present work we focus on the case of (few-site) configurations respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile. We examine the case of such “oligomers” with not only two sites, as in earlier works, but also the cases of three and four sites. While in the former case of recent experimental interest the picture of existing stationary solutions and their stability is fairly straightforward, the latter cases reveal a considerable additional complexity of solutions, including ones that exist past the linear PT-symmetry breaking point in the case of the trimer, and symmetry-breaking bifurcations, as well as more complex, even asymmetric solutions in the case of the quadrimer with nontrivial properties in their linear stability and in their nonlinear dynamics. The linearization around the obtained solutions and their dynamical evolution, when unstable, are discussed.
Disciplines
Publication Date
June 30, 2011
Publisher Statement
DOI: 10.1103/PhysRevE.83.066608
Citation Information
K. Li and Panos Kevrekidis. "PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics" Physical Review E Vol. 83 Iss. 6 (2011) Available at: http://works.bepress.com/panos_kevrekidis/239/