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

A. Hoffman; C. E. Wayne

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arXiv · 0811.2406

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

A. Hoffman·C. E. Wayne

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Abstract

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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A. Hoffman, C. E. Wayne. 2008-11-14. A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam model near the KdV Limit. https://arxiv.org/abs/0811.2406

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