Institute for Mathematics and Its Applications
Bernard Matkowsky, Northwestern University
We consider the nonlinear evolution of the coupled long scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. We derive a system of coupled complex Ginzburg-Landau and Kuramoto-Sivashinsky equations that describes the interaction between the excited monotonic mode and the excited or damped oscillatory mode, as well as a system of complex Ginzburg-Landau and Burgers equations describing the interaction of the excited oscillatory mode and the damped monotonic mode. The coupled systems are then studied, both analytically and numerically. The solutions of the coupled equations exhibit a rich variety of spatiotemporal behavior in the form of modulated standing and traveling waves, blinking states, traveling blinking states, intermittent states, heteroclinic cycles, localized chaotic structures, etc.
The talk is based on joint work with A. Golovin, A. Bayliss and A. Nepomnyashchy.