A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit
By combining results of Mizumachi and Pego on the stability of solutions for the Toda lattice with a simple rescaling and a careful control of the KdV limit we give a simple proof that small amplitude, long-wavelength solitary waves in the Fermi-Pasta-Ulam (FPU) model are linearly stable and hence by the results of Friesecke and Pego that they are also nonlinearly, asymptotically stable.
A. Hoffman was supported in part by the NSF grant DMS-0603589. C. Eugene Wayne was supported in part by the NSF grant DMS-0405724. Any findings, conclusions, opinions, or recommendations are those of the authors, and do not necessarily reflect the views of the NSF.The work reported here was completed while A. Hoffman was a member of the Department of Mathematics and Statistics, Boston University. The authors also wish to thank T. Mizumachi and R. Pego for very helpful discussions.
Received 9/12/2009; Accepted 8/23/2010