Domain wall dynamics: Growth laws, localized structures and stable droplets

We discuss the relation between the dynamics of walls separating two equivalent domains and the existence of different kinds of localized structures in systems far from thermodynamic equilibrium. In particular we focus in systems displaying a modulational instability of a. at front where an amplitude equation for the dynamics of the curvature allows to characterize different growth regimes and to predict the existence of stable droplets, localized structures whose stability comes from nonlinear curvature effects.