Coexistence of stationary and traveling waves in reaction-diffusion-advection systems

The flow- and diffusion-distributed structures (FDS) and the differential-flow instability (DIFI) are mechanisms that give rise to static and traveling waves in reactive flows with general, species-dependent transport terms. Here we consider a general framework which supports the simultaneous existence of FDS and DIFI patterns. We study the necessary conditions for each instability in general and compare them in order to derive their connection. The interaction between FDS and DIFI patterns gives rise to interesting wave behavior including stationary, upstream, and downstream traveling waves as well as an interesting regime where stationary and traveling waves coexist.