  We consider infinite FPU-type atomic chains with general convex potentials
and study the existence of monotone fronts that are heteroclinic travelling
waves connecting constant asymptotic states. Iooss showed that small amplitude
fronts bifurcate from convex-concave turning points of the force. In this paper
we prove that fronts exist for any asymptotic states that satisfy certain
constraints. For potentials whose derivative has exactly one turning point
these constraints precisely mean that the front corresponds to an energy
conserving supersonic shock of the `p-system', which is the naive hyperbolic
continuum limit of the chain. The proof goes via minimizing an action
functional for the deviation from this discontinuous shock profile. We also
discuss qualitative properties and the numerical computation of fronts.
