The accumulation of eigenvalues in a stability problem

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)70-86
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume142
Issue number1-2
DOIs
Publication statusPublished - Aug 1 2000
Externally publishedYes

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

Cite this

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

In: Physica D: Nonlinear Phenomena, Vol. 142, No. 1-2, 01.08.2000, p. 70-86.

Research output: Contribution to journalArticle

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