Coarsening to chaos-stabilized fronts.

We investigate a model for pattern formation in the presence of Galilean symmetry proposed by Matthews and Cox [Phys. Rev. E 62, R1473 (2000)], which has the form of coupled generalized Burgers- and Ginzburg-Landau-type equations. With only the system size L as a parameter, we find distinct "small-L" and "large-L" regimes exhibiting clear differences in their dynamics and scaling behavior. The long-time statistically stationary state contains a single L-dependent front, stabilized globally by spatiotemporally chaotic dynamics confined away from the front. For sufficiently large domains, the transient dynamics include a state consisting of several viscous shocklike structures that coarsens gradually, before collapsing to a single front when one front absorbs the others.