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

Michael Herrmann; Karsten Matthies

doi:10.1007/978-3-319-64173-7_1

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

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

8 Citations (SciVal)

80 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 language	English
Title of host publication	Patterns of Dynamics
Editors	Pavel Gurevich, Juliette Hell, Björn Sandstede, Arnd Scheel
Publisher	Springer
Pages	3-15
Number of pages	13
Volume	205
ISBN (Electronic)	978-3-319-64173-7
ISBN (Print)	978-3-319-64172-0
DOIs	https://doi.org/10.1007/978-3-319-64173-7_1
Publication status	Published - 8 Feb 2018
Event	International Conference on Patterns of Dynamics 2016 - Berlin, Germany Duration: 25 Jul 2016 → 29 Jul 2016

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Publisher	Springer, Cham
Volume	205
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Patterns of Dynamics 2016
Abbreviated title	PaDy 2016
Country/Territory	Germany
City	Berlin
Period	25/07/16 → 29/07/16

Keywords

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-64173-7_1

herrmannmatthies_revised
The final publication is available at Springer via: https://doi.org/10.1007/978-3-319-64173-7_1
Accepted author manuscript, 377 KBLicence: Unspecified

https://arxiv.org/abs/1611.03514v1

Cite this

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 or section in a book/report/conference proceeding › Chapter in a published conference proceeding

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

@inproceedings{37b8e7a0f4e94ffb8a0a5fe500ee489f,

title = "Uniqueness of solitary waves in the high-energy limit of FPU-type chains",

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.",

keywords = "Asymptotic analysis, FPU-type chain, High-energy limit, Lattice waves, Uniqueness of solitary waves",

author = "Michael Herrmann and Karsten Matthies",

year = "2018",

month = feb,

day = "8",

doi = "10.1007/978-3-319-64173-7_1",

language = "English",

isbn = "978-3-319-64172-0",

volume = "205",

series = " Springer Proceedings in Mathematics & Statistics",

publisher = "Springer",

pages = "3--15",

editor = "Pavel Gurevich and Hell, {Juliette } and Bj{\"o}rn Sandstede and Arnd Scheel",

booktitle = "Patterns of Dynamics",

note = "International Conference on Patterns of Dynamics 2016, PaDy 2016 ; Conference date: 25-07-2016 Through 29-07-2016",

}

TY - GEN

T1 - Uniqueness of solitary waves in the high-energy limit of FPU-type chains

AU - Herrmann, Michael

AU - Matthies, Karsten

PY - 2018/2/8

Y1 - 2018/2/8

N2 - 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.

AB - 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.

KW - Asymptotic analysis

KW - FPU-type chain

KW - High-energy limit

KW - Lattice waves

KW - Uniqueness of solitary waves

UR - http://www.scopus.com/inward/record.url?scp=85044466301&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-64173-7_1

DO - 10.1007/978-3-319-64173-7_1

M3 - Chapter in a published conference proceeding

SN - 978-3-319-64172-0

VL - 205

T3 - Springer Proceedings in Mathematics & Statistics

SP - 3

EP - 15

BT - Patterns of Dynamics

A2 - Gurevich, Pavel

A2 - Hell, Juliette

A2 - Sandstede, Björn

A2 - Scheel, Arnd

PB - Springer

T2 - International Conference on Patterns of Dynamics 2016

Y2 - 25 July 2016 through 29 July 2016

ER -

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

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this