Solitons in one-dimensional mechanical linkage

It has been shown by Kane and Lubensky that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. Although the static features of the localized modes are well captured by linearized equations of motion, the description of their dynamics requires fully nonlinear treatment. We study quasi-periodic solutions of the 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 solitons show intriguing transmission/reflection properties at the boundary of the two chains.