1D Cahn-Hilliard equation: Ostwald ripening and modulated phase systems

We use a family of stationary solutions of the Cahn-Hilliard dynamics with the aim of describing the process of coarsening during a first order phase transition. With this analytical ansatz, we can compute the characteristic time for one step of period doubling in Langer's self-similar scenario for Ostwald ripening. As an application, the same ansatz is also used to compute the thermodynamically stable period of a 1D modulated phase pattern, described by a modified Cahn-Hilliard dynamics with a long range interaction term