Instability of local deformations of an elastic rod

S. Lafortune; J. Lega

doi:10.1016/S0167-2789(03)00125-8

Instability of local deformations of an elastic rod

S. Lafortune, J. Lega

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

10 Scopus citations

Abstract

We study the instability of pulse solutions of two coupled non-linear Klein-Gordon equations by means of Evans function techniques. The system of coupled Klein-Gordon equations considered here describes the near-threshold dynamics of a three-dimensional elastic rod with circular cross-section, subject to constant twist. We determine a condition on the speed of the traveling pulse which ensures spectral instability.

Original language	English (US)
Pages (from-to)	103-124
Number of pages	22
Journal	Physica D: Nonlinear Phenomena
Volume	182
Issue number	1-2
DOIs	https://doi.org/10.1016/S0167-2789(03)00125-8
State	Published - Aug 1 2003

Keywords

Elastic rod
Evans function
Klein-Gordon equations

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(03)00125-8

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title = "Instability of local deformations of an elastic rod",

abstract = "We study the instability of pulse solutions of two coupled non-linear Klein-Gordon equations by means of Evans function techniques. The system of coupled Klein-Gordon equations considered here describes the near-threshold dynamics of a three-dimensional elastic rod with circular cross-section, subject to constant twist. We determine a condition on the speed of the traveling pulse which ensures spectral instability.",

keywords = "Elastic rod, Evans function, Klein-Gordon equations",

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

note = "Funding Information: We are grateful to M. Agrotis, N. Ercolani, A. Espi{\~n}ola-Rocha, A. Goriely and R. Indik for useful discussions. Most of the calculations presented in this paper would not have been possible without the help of MAPLE (Waterloo Maple Inc.). One of the authors, SL acknowledges a postdoctoral fellowship from NSERC (National Science and Engineering Research Council) of Canada. This material is based upon work supported by the National Science Foundation under Grant No. DMS-0075827 to JL. ",

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T1 - Instability of local deformations of an elastic rod

AU - Lafortune, S.

AU - Lega, J.

N1 - Funding Information: We are grateful to M. Agrotis, N. Ercolani, A. Espiñola-Rocha, A. Goriely and R. Indik for useful discussions. Most of the calculations presented in this paper would not have been possible without the help of MAPLE (Waterloo Maple Inc.). One of the authors, SL acknowledges a postdoctoral fellowship from NSERC (National Science and Engineering Research Council) of Canada. This material is based upon work supported by the National Science Foundation under Grant No. DMS-0075827 to JL.

PY - 2003/8/1

Y1 - 2003/8/1

N2 - We study the instability of pulse solutions of two coupled non-linear Klein-Gordon equations by means of Evans function techniques. The system of coupled Klein-Gordon equations considered here describes the near-threshold dynamics of a three-dimensional elastic rod with circular cross-section, subject to constant twist. We determine a condition on the speed of the traveling pulse which ensures spectral instability.

AB - We study the instability of pulse solutions of two coupled non-linear Klein-Gordon equations by means of Evans function techniques. The system of coupled Klein-Gordon equations considered here describes the near-threshold dynamics of a three-dimensional elastic rod with circular cross-section, subject to constant twist. We determine a condition on the speed of the traveling pulse which ensures spectral instability.

KW - Elastic rod

KW - Evans function

KW - Klein-Gordon equations

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-2

ER -

Instability of local deformations of an elastic rod

Abstract

Keywords

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