TY - JOUR

T1 - Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems

AU - Bernoff, A. J.

AU - Kuske, R.

AU - Matkowsky, Bernard J

AU - Volpert, V.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0029292815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029292815&partnerID=8YFLogxK

U2 - 10.1137/S0036139993269308

DO - 10.1137/S0036139993269308

M3 - Article

AN - SCOPUS:0029292815

SN - 0036-1399

VL - 55

SP - 485

EP - 519

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 2

ER -