耦合DNLS晶格中的交错孤子和涡旋
Interlaced solitons and vortices in coupled DNLS lattices
摘要：
在本论文中，我们提出了一组新的相干结构，这种相干结构出现在具有多个分量的非线性动力学晶格中，即交错孤子。这些是在相关反连续极限中的波形，即，当位点未耦合时，一个分量具有支撑，而另一个分量不具有支撑。我们系统地说明了如何可以结合动态稳定的一元模式，以创建这样的二进制情况下的两个组件。在一维的设置，我们还提供了一个详细的理论分析，这些波形的存在和稳定性，而在更高的维度，这样的分析计算是远远更多的参与，我们诉诸于相应的数值计算。最后，我们进行直接的数值模拟，以展示这些结构如何打破，当指数或不稳定，结构与参与网站的数量较少。
英文摘要：
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e. when the sites are uncoupled, one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create ones such for the binary case of two-components. In the one-dimensional setting, we provide also a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.
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