Exact solutions of a model for granular avalanches

We present exact solutions of the non-linear BCRE model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slopes. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced. Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, and velocities of the active region and of the sandpile profile.