Traveling Waves for Monomer Chains with Pre-compression

In the present work, we complement our earlier study on the subject of granular crystals in the purely nonlinear limit (no precompression) by considering the case where an underlying linear limit exists (finite precompression). In the latter context, we explicitly prove the existence of supersonic traveling waves, which are smooth, positive and exponentially localized. While numerical computations suggest that the cutoff point for the existence of such exponentially decaying waves is exactly the speed of sound in the system, we can not establish this result sharply within our variational technique but can only prove a relevant upper bound on the propagation speed of bell-shaped traveling waves.