High-energy waves in superpolynomial FPU-type chains

Abstract

We consider periodic traveling waves in FPU-type chains with superpolynomial interaction forces and derive explicit asymptotic formulas for the high-energy limit as well as bounds for the corresponding approximation error. In the proof we adapt twoscale techniques that have recently been develop by Herrmann and Matthies for chains with singular potential and provide an asymptotic ODE for the scaled distance profile.

revised version with minor changes (corrected typos, further references); 22 pages, 4 figures

References in corpus (1)

• Counterpropagating Two-Soliton Solutions in the FPU Lattice

Cited by in corpus (4)

• Waves in Strongly Nonlinear Gardner-like Equations on a Lattice
• Solitary waves in atomic chains and peridynamical media
• Nonlinear and Nonlocal Eigenvalue Problems
• Uniqueness of solitary waves in the high-energy limit of FPU-type chains