PT-对称低聚物：解析解、线性稳定性和非线性动力学
PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics
摘要：
在目前的工作中，我们专注于（少数网站）配置尊重PT对称性的情况下。我们研究的情况下，这样的“低聚物”不仅与2-网站，在早期的作品，但也有3-和4-网站的情况下。而在前一种情况下，最近的实验兴趣，现有的固定的解决方案和他们的稳定性的图片是相当简单的，后者的情况下，揭示了相当多的额外的复杂性的解决方案，包括存在过去的线性PT-断点的情况下的三聚体，更复杂的，甚至不对称的解决方案的情况下的四聚体与非平凡的光谱和动力学性质。讨论了所得到解的线性稳定性和非线性动力学性质。
英文摘要：
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.
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