High-energy waves in superpolynomial FPU-type chains

TL;DR

This paper analyzes high-energy periodic traveling waves in FPU chains with superpolynomial forces, deriving explicit asymptotics and error bounds using advanced two-scale techniques and asymptotic ODEs.

Contribution

It introduces new asymptotic formulas and bounds for high-energy waves in superpolynomial FPU chains, adapting recent two-scale methods for singular potentials.

Findings

Explicit asymptotic formulas for high-energy waves

Bounds on approximation errors in the asymptotics

Asymptotic ODE for scaled distance profile

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.