  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.
