2011/02/03 by K. Li, P. G. Kevrekidis · 145 citations
Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Computer science #Focus (optics) #Geometry #Linearization #Machine learning #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Stability (learning theory) #Symmetry (geometry) #Symmetry breaking #Trimer #cond-mat.quant-gas #nlin.PS
paper · pdf · doi:10.1103/physreve.83.066608
published in Physical Review E 83(6), 066608 (American Physical Society) · 6 pages, 9 figures
arxiv created 2011/02/03 · openalex publication_date 2011/06/30 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.