六角形和蜂窝格子中的离散孤子和涡旋：存在性、稳定性和动力学
Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics
摘要：
我们考虑一个典型的动力学晶格模型，即非正方晶格几何上的离散非线性薛定谔方程。我们提出了一个系统的分类的解决方案，出现在主要的六格网站和三格网站的轮廓的形式都离散多极孤子和离散涡。除了识别可能的状态，我们分析跟踪其线性稳定性定性和定量。我们发现，在六格位形中，交替相的六极和拓扑荷S=2的涡旋具有稳定区间;在三格位形中，只有拓扑荷S=1的涡旋在聚焦非线性情况下可能是稳定的.通过对反连续极限的定态进行详细的数值分叉分析，以及通过直接模拟来监控动力学不稳定性（当后者出现时），这些结论对于六边形和蜂窝晶格都得到了证实。动力学揭示了丰富的非线性行为，不仅在单站点孤立波的形式，但也在强大的多站点呼吸结构。
英文摘要：
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the hexapole of alternating phases, as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.
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