PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics

TL;DR

This paper investigates PT-symmetric oligomers with 2, 3, and 4 sites, analyzing their stationary solutions, stability, and nonlinear dynamics, revealing complex behaviors including solutions beyond the linear PT-breaking point.

Contribution

It extends the analysis of PT-symmetric oligomers to 3- and 4-site configurations, uncovering new solution types and stability properties not previously explored.

Findings

Existence of solutions beyond the linear PT-breaking point in trimers.

Complex, asymmetric solutions in quadrimers with unique spectral properties.

Detailed stability and dynamical analysis of multi-site PT-symmetric systems.

Abstract

In the present work we focus on the case of (few-site) configurations respecting the PT-symmetry. We examine the case of such "oligomers" with not only 2-sites, as in earlier works, but also the cases of 3- and 4-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-breaking point in the case of the trimer, and more complex, even asymmetric solutions in the case of the quadrimer with nontrivial spectral and dynamical properties. Both the linear stability and the nonlinear dynamical properties of the obtained solutions are discussed.