It is well established that the solitary waves of FPU-type chains converge in
the high-energy limit to traveling waves of the hard-sphere model. In this
paper we establish improved asymptotic expressions for the wave profiles as
well as an explicit formula for the wave speed. The key step in our approach is
the derivation of an asymptotic ODE for the appropriately rescaled strain
profile.Comment: revised version with corrected typos; 25 pages, several figure
