Spectral stability of local deformations of an elastic rod: Hamiltonian formalism

S. Lafortune; J. Lega

doi:10.1137/S0036141004439350

Spectral stability of local deformations of an elastic rod: Hamiltonian formalism

S. Lafortune, J. Lega

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Hamiltonian methods are used to obtain a necessary and sufficient condition for the spectral stability of pulse solutions to two coupled nonlinear Klein-Gordon equations. These equations describe the near-threshold dynamics of an elastic rod with circular cross section. The present work completes and extends a recent analysis of the authors' [Phys. D, 182 (2003), pp. 103-124], in which a sufficient condition for the instability of "nonrotating" pulses was found by means of Evans function techniques.

Original language	English (US)
Pages (from-to)	1726-1741
Number of pages	16
Journal	SIAM Journal on Mathematical Analysis
Volume	36
Issue number	6
DOIs	https://doi.org/10.1137/S0036141004439350
State	Published - 2005

Keywords

Elastic filament
Hamiltonian methods
Spectral stability

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/S0036141004439350

Cite this

@article{f33138293fbe465a959fd3d5df34c3b5,

title = "Spectral stability of local deformations of an elastic rod: Hamiltonian formalism",

abstract = "Hamiltonian methods are used to obtain a necessary and sufficient condition for the spectral stability of pulse solutions to two coupled nonlinear Klein-Gordon equations. These equations describe the near-threshold dynamics of an elastic rod with circular cross section. The present work completes and extends a recent analysis of the authors' [Phys. D, 182 (2003), pp. 103-124], in which a sufficient condition for the instability of {"}nonrotating{"} pulses was found by means of Evans function techniques.",

keywords = "Elastic filament, Hamiltonian methods, Spectral stability",

author = "S. Lafortune and J. Lega",

year = "2005",

doi = "10.1137/S0036141004439350",

language = "English (US)",

volume = "36",

pages = "1726--1741",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "6",

}

TY - JOUR

T1 - Spectral stability of local deformations of an elastic rod

T2 - Hamiltonian formalism

AU - Lafortune, S.

AU - Lega, J.

PY - 2005

Y1 - 2005

N2 - Hamiltonian methods are used to obtain a necessary and sufficient condition for the spectral stability of pulse solutions to two coupled nonlinear Klein-Gordon equations. These equations describe the near-threshold dynamics of an elastic rod with circular cross section. The present work completes and extends a recent analysis of the authors' [Phys. D, 182 (2003), pp. 103-124], in which a sufficient condition for the instability of "nonrotating" pulses was found by means of Evans function techniques.

AB - Hamiltonian methods are used to obtain a necessary and sufficient condition for the spectral stability of pulse solutions to two coupled nonlinear Klein-Gordon equations. These equations describe the near-threshold dynamics of an elastic rod with circular cross section. The present work completes and extends a recent analysis of the authors' [Phys. D, 182 (2003), pp. 103-124], in which a sufficient condition for the instability of "nonrotating" pulses was found by means of Evans function techniques.

KW - Elastic filament

KW - Hamiltonian methods

KW - Spectral stability

UR - http://www.scopus.com/inward/record.url?scp=27844536860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27844536860&partnerID=8YFLogxK

U2 - 10.1137/S0036141004439350

DO - 10.1137/S0036141004439350

M3 - Article

AN - SCOPUS:27844536860

SN - 0036-1410

VL - 36

SP - 1726

EP - 1741

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

Spectral stability of local deformations of an elastic rod: Hamiltonian formalism

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this