Coupled KS-CGL and coupled Burgers-CGL equations for flames governed by a sequential reaction

We consider the nonlinear evolution of the coupled long-scale oscillatory a nd monotonic instabilities of a uniformly propagating combustion wave gover ned by a sequential chemical reaction, having two flame fronts correspondin g 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 mod e and the excited or damped oscillatory mode, as well as a system of comple x Ginzburg-Landau and Burgers equations describing the interaction of the e xcited oscillatory mode and the damped monotonic mode. The coupled systems are then studied, both analytically and numerically. The solutions of the c oupled equations exhibit a rich variety of spatio-temporal behavior in the form of modulated standing and traveling waves, blinking states, traveling blinking states, intermittent states, heteroclinic cycles, strange attracto rs, etc. (C) 1999 Elsevier Science B.V. All rights reserved.