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By combining results of Mizumachi on the stability of solitons for the Todalattice with a simple rescaling and a careful control of the KdV limit we givea simple proof that small amplitude, long-wavelength solitary waves in theFermi-Pasta-Ulam (FPU) model are linearly stable and hence by the results ofFriesecke and Pego that they are also nonlinearly, asymptotically stable.

A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam model near the KdV Limit