Uniqueness of solitary waves in the high-energy limit of FPU-type chains

Michael Herrmann, Karsten Matthies

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Downloads (Pure)

Abstract

Recent asymptotic results by the authors 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.
Original languageEnglish
Title of host publicationPatterns of Dynamics
EditorsPavel Gurevich, Juliette Hell, Björn Sandstede, Arnd Scheel
PublisherSpringer
Pages3-15
Number of pages13
Volume205
ISBN (Electronic)978-3-319-64173-7
ISBN (Print)978-3-319-64172-0
DOIs
Publication statusE-pub ahead of print - 8 Feb 2018
EventInternational Conference on Patterns of Dynamics 2016 - Berlin, Germany
Duration: 25 Jul 201629 Jul 2016

Publication series

Name Springer Proceedings in Mathematics & Statistics
PublisherSpringer, Cham
Volume205
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Patterns of Dynamics 2016
Abbreviated titlePaDy 2016
CountryGermany
CityBerlin
Period25/07/1629/07/16

Fingerprint

Solitary Waves
Traveling Wave
High Energy
Uniqueness
Delay Differential Equations
Linear differential equation
Asymptotic Analysis
Linearization
Eigenfunctions
Wave equation
Eigenvalue
Symmetry
Imply
Zero

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Herrmann, M., & Matthies, K. (2018). Uniqueness of solitary waves in the high-energy limit of FPU-type chains. In P. Gurevich, J. Hell, B. Sandstede, & A. Scheel (Eds.), Patterns of Dynamics (Vol. 205, pp. 3-15). ( Springer Proceedings in Mathematics & Statistics; Vol. 205). Springer. https://doi.org/10.1007/978-3-319-64173-7_1

Uniqueness of solitary waves in the high-energy limit of FPU-type chains. / Herrmann, Michael; Matthies, Karsten.

Patterns of Dynamics . ed. / Pavel Gurevich; Juliette Hell; Björn Sandstede; Arnd Scheel. Vol. 205 Springer, 2018. p. 3-15 ( Springer Proceedings in Mathematics & Statistics; Vol. 205).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Herrmann, M & Matthies, K 2018, Uniqueness of solitary waves in the high-energy limit of FPU-type chains. in P Gurevich, J Hell, B Sandstede & A Scheel (eds), Patterns of Dynamics . vol. 205, Springer Proceedings in Mathematics & Statistics, vol. 205, Springer, pp. 3-15, International Conference on Patterns of Dynamics 2016, Berlin, Germany, 25/07/16. https://doi.org/10.1007/978-3-319-64173-7_1
Herrmann M, Matthies K. Uniqueness of solitary waves in the high-energy limit of FPU-type chains. In Gurevich P, Hell J, Sandstede B, Scheel A, editors, Patterns of Dynamics . Vol. 205. Springer. 2018. p. 3-15. ( Springer Proceedings in Mathematics & Statistics). https://doi.org/10.1007/978-3-319-64173-7_1
Herrmann, Michael ; Matthies, Karsten. / Uniqueness of solitary waves in the high-energy limit of FPU-type chains. Patterns of Dynamics . editor / Pavel Gurevich ; Juliette Hell ; Björn Sandstede ; Arnd Scheel. Vol. 205 Springer, 2018. pp. 3-15 ( Springer Proceedings in Mathematics & Statistics).
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