Pressure Fronts in 1D Damped Nonlinear Lattices

The propagation of pressure fronts (impact solutions) in 1D chains of atoms coupled by anharmonic potentials between nearest neighbor and submitted to damping forces preserving uniform motion, is investigated. Travelling fronts between two regions at different uniform pressures are found numerically and well approximate analytically. It is proven that there are three analytical relations between the impact velocity, the compression, the front velocity and the energy dissipation which only depend on the coupling potential and are $\mathit{\text{independent}}$ of the damping. Such travelling front solutions cannot exist without damping.