Traveling waves in phase-separating reactive mixtures

A model of phase separation of chemically reactive ternary mixtures is constructed. In this model, spatially periodic structures that coherently propagate at a constant speed emerge through a Hopf bifurcation at a finite wave number. It is shown by computer simulations that both lamellar and hexagonal structures undergo a coherent propagating motion in two dimensions, and there are two types of traveling hexagons depending on the relative direction between the traveling velocity and the lattice vectors of the hexagonal structure. Amplitude equations for the traveling waves are derived, and the stability of the traveling and standing waves is discussed.