Instability of local deformations of an elastic rod: Numerical evaluation of the evans function

S. Lafortune, J. Lega, S. Madrid

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We present a method for the numerical evaluation of the Evans function that doesnot require integration in an associated exterior algebra space. This technique is suitable for thedetection of bifurcations and is particularly useful when the dimension of the linearized systemand/or the dimension of the converging subspaces at infinity is large. We test this approach byinvestigating the stability of a two-parameter family of traveling pulse solutions to two coupledKlein-Gordon equations. The spectral stability of these pulses is completely understood analytically [S. Lafortune and J. Lega, SIAM J. Math. Anal. , 36 (2005), pp. 1726-1741], and we show that ournumerical method is able to detect bifurcations of the pulse family with very good accuracy.

Original languageEnglish (US)
Pages (from-to)1653-1672
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume71
Issue number5
DOIs
StatePublished - Nov 14 2011

Keywords

  • Elastic rod
  • Evans function
  • Klein-Gordon equations
  • Numerical method

ASJC Scopus subject areas

  • Applied Mathematics

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