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Stable droplets and growth laws close to the modulational instability of a domain wall

Gomila, Damià; Colet, Pere; Oppo, Gian-Luca; San Miguel, Maxi
Physical Review Letters 87, 194101 (1-4) (2001)

We consider the curvature driven dynamics of a domain wall separating two
equivalent states in systems displaying a modulational instability of a flat
front. We derive an amplitude equation for the dynamics of the curvature
close to the bifurcation point from growing to shrinking circular droplets.
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) ~ t^1/4 is
obtained. Our general analytical predictions, which are valid for a wide
variety of systems including models of nonlinear optical cavities and
reaction-diffusion systems, are illustrated in the parametrically driven
complex Ginzburg-Landau equation.