  The confining pressure $P$ is perhaps the most important parameter
controlling the properties of granular matter. Strongly compressed granular
media are, in many respects, simple solids in which elastic perturbations
travel as ordinary phonons. However, the speed of sound in granular aggregates
continuously decreases as the confining pressure decreases, completely
vanishing at the jamming-unjamming transition. This anomalous behavior suggests
that the transport of energy at low pressures should not be dominated by
phonons. In this work we use simulations and theory to show how the response of
granular systems becomes increasingly nonlinear as pressure decreases. In the
low pressure regime the elastic energy is found to be mainly transported
through nonlinear waves and shocks. We numerically characterize the propagation
speed, shape, and stability of these shocks, and model the dependence of the
shock speed on pressure and impact intensity by a simple analytical approach.
