论文标题
晶格中的色散冲击波：降低尺寸的方法
Dispersive Shock Waves in Lattices: A Dimension Reduction Approach
论文作者
论文摘要
分散冲击波（DSWS）通过调制波列连接不同振幅的状态，该状态通常在发生状态突然变化的非线性色散介质中形成。 DSWS分析研究的主要工具是Whitham的调制理论。尽管该框架已成功地用于许多空间连续设置来描述DSW，但在大多数空间离散系统中，Whitham调制方程实际上是可悲的。在本文中，我们说明了在广泛的晶格示例中减少DSW动力学与平面颂歌的相关性。这种低维极的溶液准确地描述了与调制方程一致的方式，在自相似坐标和局部平均值中DSW的轨道。我们在离散的保护定律系统中使用数据驱动和准核心方法来证明如何确定和分析DSW的基础低维结构。还讨论了这些结果与Whitham调制理论的联系。
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is Whitham's modulation theory. While this framework has been successfully employed in many space-continuous settings to describe DSWs, the Whitham modulation equations are virtually intractable in most spatially discrete systems. In this article, we illustrate the relevance of the reduction of the DSW dynamics to a planar ODE in a broad class of lattice examples. Solutions of this low-dimensional ODE accurately describe the orbits of the DSW in self-similar coordinates and the local averages in a manner consistent with the modulation equations. We use data-driven and quasi-continuum approaches within the context of a discrete system of conservation laws to demonstrate how the underlying low dimensional structure of DSWs can be identified and analyzed. The connection of these results to Whitham modulation theory is also discussed.
