  We study the dynamics of solitary waves traveling in a one-dimensional chain
of bistable elements in the presence of a local inhomogeneity (defect).
Numerical simulations reveal that depending upon its initial speed, an incoming
solitary wave can get transmitted, captured or reflected upon interaction with
the defect. The dynamics are dominated by energy exchange between the wave and
a breather mode localized at the defect. We derive a reduced-order two degree
of freedom Hamiltonian model for wave-breather interaction, and analyze it
using dynamical systems techniques. Lobe dynamics analysis reveals the fine
structure of phase space that leads to the complicated dynamics in this system.
This work is a step towards developing a rational approach to defect
engineering for manipulating nonlinear waves in mechanical metamaterials.

Chaotic Dynamics;Soft Condensed Matter;Analysis of PDEs;Dynamical Systems