  We study the growth of a periodic pattern in one dimension for a model of
spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on
the intermediate region, where the non-linearity cannot be negected anymore,
and before the coalescence dominates. The dynamics is captured through the
standard technique of a solubility condition performed over a particular family
of quasi-static solutions. The main result is that the dynamics along this
particular class of solutions can be expressed in terms of a simple ordinary
differential equation. The density profile of the stationary regime found at
the end of the non-linear growth is also well characterized. Numerical
simulations correspond satisfactorily to the analytical results through three
different methods and asymptotic dynamics are well recovered, even far from the
region where the approximations hold.
