  We give a rigorous proof of existence for solitary waves of a peridynamics
model in one space dimension recently investigated by Silling (J. Mech. Phys.
Solids 96:121--132, 2016). We adapt the variational framework developed by
Friesecke and Wattis (Comm. Math Phys. 161:391--418, 1994) for the
Fermi-Pasta-Ulam-Tsingou lattice equations to treat a truncated problem which
cuts off short-range interactions, then pass to the limit.
