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

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

2008-11-14

arxiv.org/abs/0811.2406v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

By combining results of Mizumachi on the stability of solitons 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.

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