论文标题
晶格动力学系统中的空间局部结构
Spatially Localized Structures in Lattice Dynamical Systems
论文作者
论文摘要
我们研究表现出双态性的晶格动力系统中的固定，空间局部的模式。与这些模式相关的轮廓具有较长的平稳状态，该模式类似于Bistable状态之一，而该轮廓靠近该高原以外的第二个Biscable状态。我们表明，这种模式的存在分支通常形成一个无限的封闭环（ISLAS）或缠绕的S形曲线（蛇）的堆栈。然后，我们使用抗Continuum极限附近的分叉理论，在晶格中，边缘之间的耦合消失，以证明存在壳的存在，并在可靠近的离散离散的真实Ginzburg-landau方程中。我们还提供了数值证据，证明存在正方形和六角形晶格上平面局部贴片的蛇图，并概述了严格分析它们的策略。
We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where the pattern resembles one of the bistable states, while the profile is close to the second bistable state outside this plateau. We show that the existence branches of such patterns generically form either an infinite stack of closed loops (isolas) or intertwined s-shaped curves (snaking). We then use bifurcation theory near the anti-continuum limit, where the coupling between edges in the lattice vanishes, to prove existence of isolas and snaking in a bistable discrete real Ginzburg--Landau equation. We also provide numerical evidence for the existence of snaking diagrams for planar localized patches on square and hexagonal lattices and outline a strategy to analyse them rigorously.
