Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

TL;DR

This paper derives improved asymptotic formulas for solitary waves in FPU chains at high energy, providing explicit wave speed formulas and an asymptotic ODE for the strain profile, advancing understanding of wave behavior in these systems.

Contribution

It introduces refined asymptotic expressions and an explicit wave speed formula for high-energy solitary waves in FPU chains, based on an asymptotic ODE for the strain profile.

Findings

Derived improved asymptotic wave profiles

Provided explicit formulas for wave speed

Established an asymptotic ODE for the strain profile

Abstract

It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an explicit formula for the wave speed. The key step in our approach is the derivation of an asymptotic ODE for the appropriately rescaled strain profile.