Stable droplets and growth laws close to the modulational instability of adomain wall - art. no. 194101

We consider the curvature driven dynamics of a domain wall separating two e quivalent states in systems displaying a modulational instability of a flat front. An amplitude equation for the dynamics of the curvature close to th e bifurcation point from growing to shrinking circular droplets is derived. We predict the existence of stable droplets with a radius R that diverges at the bifurcation point, where a curvature driven growth law R(t) approxim ate to t(1/4) is obtained. Our general analytical predictions, which are va lid for a wide variety of systems including models of nonlinear optical cav ities and reaction-diffusion systems are illustrated in the parametrically driven complex Ginzburg-Landau equation.