  We study atomic chains with nonlinear nearest neighbour interactions and
prove the existence of fronts (heteroclinic travelling waves with constant
asymptotic states). Generalizing recent results of Herrmann and Rademacher we
allow for non-convex interaction potentials and find fronts with non-monotone
profile. These fronts minimize an action integral and can only exists if the
asymptotic states fulfil the macroscopic constraints and if the interaction
potential satisfies a geometric graph condition. Finally, we illustrate our
findings by numerical simulations.
