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Uniqueness of Solitary Waves in the High-Energy Limit of FPU-Type Chains

  • Michael Herrmann
  • Karsten Matthies
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 205)

Abstract

Recent asymptotic results in [12] provided detailed information on the shape of solitary high-energy travelling waves in FPU atomic chains. In this note we use and extend the methods to understand the linearisation of the travelling wave equation. We show that there are not any other zero eigenvalues than those created by the translation symmetry and this implies a local uniqueness result. The key argument in our asymptotic analysis is to replace the linear advance-delay-differential equation for the eigenfunctions by an approximate ODE.

Keywords

Lattice waves High-energy limit FPU-type chain Uniqueness of solitary waves Asymptotic analysis 

Mathematics Subject Classification:

37K60 37K40 74H10 

Notes

Acknowledgements

The authors are grateful for the support by the Deutsche Forschungsgemeinschaft (DFG individual grant HE 6853/2-1) and the London Mathematical Society (LMS Scheme 4 Grant, Ref 41326). KM would like to thank for the hospitality during a sabbatical stay at the University of Münster.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für Numerische und Angewandte MathematikWestfälische Wilhelms-Universität MünsterMünsterGermany
  2. 2.Department of Mathematical SciencesUniversity of BathBathUK

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