An extension of the stability index for traveling-wave solutions and its application to bifurcations

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Abstract

We treat the stability index for traveling-wave solutions of one-dimensional reaction-diffusion equations due to Alexander, Gardner, and Jones [J. Reine Angew. Math., 410(1990), pp. 167-212]. An extension of the stability index which makes the index robust to perturbation is given and, using the extension, an additive formula for a gluing bifurcation of traveling waves is proven. We also consider certain heteroclinic bifurcations as an application, some specific examples of which are discussed.

Original languageEnglish
Pages (from-to)402-433
Number of pages32
JournalSIAM Journal on Mathematical Analysis
Volume28
Issue number2
DOIs
Publication statusPublished - Mar 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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