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.
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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 -