一维机械连杆机构中的孤子
Solitons in one-dimensional mechanical linkage
摘要：
人们已经观察到，某些经典的链承认拓扑保护的零能量模式是本地化的边界上。这种局域模式的静态特征被捕获的线性化运动方程，但其动态特征是由它的非线性。研究一维经典链非线性运动方程的拟周期解。这样的准周期解对应于离散系统的配置空间中的周期轨迹，这使得我们可以定义孤子，而不依赖于连续理论。此外，我们研究了孤子在非均匀系统中的动力学，通过连接两个链与不同的参数集，其中孤子的传输或反射发生在两个链的边界。
英文摘要：
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the dynamical features are governed by its nonlinearity. We study quasi-periodic solutions of nonlinear equations of motion of one-dimensional classical chains. Such quasi-periodic solutions correspond to periodic trajectories in the configuration space of the discrete systems, which allows us to define solitons without relying on a continuum theory. Furthermore, we study the dynamics of solitons in inhomogeneous systems by connecting two chains with distinct parameter sets, where transmission or reflection of solitons occurs at the boundary of the two chains.
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