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

2008/11/14 by A. Hoffman, C. Eugene Wayne, Hoffman, A. +1
Physics and Astronomy · Mathematics · #Nonlinear Photonic Systems #Advanced Mathematical Physics Problems #Cold Atom Physics and Bose-Einstein Condensates

paper · pdf · doi:10.48550/arxiv.0811.2406

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.

Related

• Long-time stability of small FPU solitary waves
• Transition from Solitons to Solitary Waves in the Fermi-Pasta-Ulam Lattice
• N-soliton states of the FPU lattices
• Unstable dynamics of solitary traveling waves in a lattice with long-range interactions
• L²-stability of solitary waves for the KdV equation via Pego and Weinstein's method