The accumulation of eigenvalues in a stability problem

研究成果: ジャーナルへの寄稿記事

9 引用 (Scopus)

抄録

When two waves propagating in a one-dimensional medium are locked together as a composite wave, a natural question arises as to whether the new wave is stable. An interesting and novel instability mechanism is exposed here in which a cascade of eigenvalues accumulates at a distinguished point in the unstable half plane. The underlying assumption is that the transition between the two waves occurs at an unstable, homogeneous steady state of the partial differential equations. This causes the individual waves to have an unstable continuous spectrum, but the instability of the full wave cannot be predicted from the configuration of these spectra alone.

元の言語英語
ページ(範囲)70-86
ページ数17
ジャーナルPhysica D: Nonlinear Phenomena
142
発行部数1-2
DOI
出版物ステータス出版済み - 8 1 2000
外部発表Yes

Fingerprint

eigenvalues
half planes
continuous spectra
partial differential equations
cascades
composite materials
causes
configurations

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

これを引用

The accumulation of eigenvalues in a stability problem. / Nii, Shunsaku.

:: Physica D: Nonlinear Phenomena, 巻 142, 番号 1-2, 01.08.2000, p. 70-86.

研究成果: ジャーナルへの寄稿記事

@article{ed2990603c50430298050d46ab303ccc,
title = "The accumulation of eigenvalues in a stability problem",
abstract = "When two waves propagating in a one-dimensional medium are locked together as a composite wave, a natural question arises as to whether the new wave is stable. An interesting and novel instability mechanism is exposed here in which a cascade of eigenvalues accumulates at a distinguished point in the unstable half plane. The underlying assumption is that the transition between the two waves occurs at an unstable, homogeneous steady state of the partial differential equations. This causes the individual waves to have an unstable continuous spectrum, but the instability of the full wave cannot be predicted from the configuration of these spectra alone.",
author = "Shunsaku Nii",
year = "2000",
month = "8",
day = "1",
doi = "10.1016/S0167-2789(00)00061-0",
language = "English",
volume = "142",
pages = "70--86",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - The accumulation of eigenvalues in a stability problem

AU - Nii, Shunsaku

PY - 2000/8/1

Y1 - 2000/8/1

N2 - When two waves propagating in a one-dimensional medium are locked together as a composite wave, a natural question arises as to whether the new wave is stable. An interesting and novel instability mechanism is exposed here in which a cascade of eigenvalues accumulates at a distinguished point in the unstable half plane. The underlying assumption is that the transition between the two waves occurs at an unstable, homogeneous steady state of the partial differential equations. This causes the individual waves to have an unstable continuous spectrum, but the instability of the full wave cannot be predicted from the configuration of these spectra alone.

AB - When two waves propagating in a one-dimensional medium are locked together as a composite wave, a natural question arises as to whether the new wave is stable. An interesting and novel instability mechanism is exposed here in which a cascade of eigenvalues accumulates at a distinguished point in the unstable half plane. The underlying assumption is that the transition between the two waves occurs at an unstable, homogeneous steady state of the partial differential equations. This causes the individual waves to have an unstable continuous spectrum, but the instability of the full wave cannot be predicted from the configuration of these spectra alone.

UR - http://www.scopus.com/inward/record.url?scp=0345848729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345848729&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(00)00061-0

DO - 10.1016/S0167-2789(00)00061-0

M3 - Article

VL - 142

SP - 70

EP - 86

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -