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.
ASJC Scopus subject areas
- Applied Mathematics