Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems

A. J. Bernoff*, R. Kuske, B. J. Matkowsky, V. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

A system of reaction-diffusion equations with a traveling wave solution was considered as a basic state to investigate the scenario of counterpropagating traveling wave solutions of reaction-diffusion systems. We determined solutions bifurcating from the basic state that described counterpropagating traveling waves in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, we derived long wave modulation equations for the amplitudes of the counterpropagating traveling waves that were coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations were then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves.

Original languageEnglish (US)
Pages (from-to)485-519
Number of pages35
JournalSIAM Journal on Applied Mathematics
Volume55
Issue number2
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Applied Mathematics

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