Paper

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

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Published 10 July 2015 • © 2015 IOP Publishing Ltd & London Mathematical Society
, , Citation Michael Herrmann and Karsten Matthies 2015 Nonlinearity 28 2767 DOI 10.1088/0951-7715/28/8/2767

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Author e-mails

michael.herrmann@uni-muenster.de

k.matthies@maths.bath.ac.uk

Author affiliations

1 Institut für Numerische und Angewandte Mathematik, Universität Münster, Einsteinstraße 62, D-48149 Münster, Germany

2 Department of Mathematical Sciences, University of Bath, BA2 7AY Bath,UK

Dates

  1. Received 19 February 2015
  2. Accepted 25 May 2015
  3. Published

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0951-7715/28/8/2767

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.

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10.1088/0951-7715/28/8/2767