二维动力学格点上超越最近邻相互作用的剧烈作用：一个例子
The Drastic Role of Beyond Nearest-Neighbor Interactions on Two-Dimensional Dynamical Lattices: A Case Example
摘要：
在目前的工作中，我们强调的显着效果，最简单的超越最近邻相互作用可以在二维动力学晶格。为此，我们选择最近的进一步邻居，即对角的，和一个典型的非线性晶格，离散的非线性薛定谔方程作为我们的案例。仅仅改变这种额外的邻居相互作用的强度，我们看到的例子是：（a）在最近邻居极限中开始稳定的状态的不稳定;（b）在该极限中开始不稳定的状态的稳定;（c）在最近邻居情况下不存在的新状态的分叉。这些戏剧性的变化首先在理论上强调通过分析减少的问题，一些兴奋的网站和相关的一套条件，管理他们的存在和他们的动态稳定性。然后，通过不动点计算，频谱分析和非线性动力学演化模拟，他们证实了数字。
英文摘要：
In the present work, we highlight the significant effect that the simplest beyond nearest neighbor interactions can have on two-dimensional dynamical lattices. To do so, we select as our case example the closest further neighbor, namely the diagonal one, and a prototypical nonlinear lattice, the discrete nonlinear Schrodinger equation. Varying solely the strength of this extra neighbor interaction, we see examples of (a) destabilization of states that start out as stable in the nearest neighbor limit; (b) stabilization of states that start out as unstable in that limit; (c) bifurcation of novel states that do not exist in the nearest neighbor case. These dramatic changes are first theoretically highlighted through an analysis of a reduction of the problem to a few excited sites and the associated set of conditions that govern their existence and their dynamical stability. Then, they are corroborated numerically through fixed point computations, spectral analysis and nonlinear dynamical evolution simulations.
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