  Nonlinear effects on the early stage of phase ordering are studied using
Adomian's decomposition method for the Ginzburg-Landau equation for a
nonconserved order parameter. While the long-time regime and the linear
behavior at short times of the theory are well understood, the onset of
nonlinearities at short times and the breaking of the linear theory at
different length scales are less understood. In the Adomian's decomposition
method, the solution is systematically calculated in the form of a polynomial
expansion for the order parameter, with a time dependence given as a series
expansion. The method is very accurate for short times, which allows to
incorporate the short-time dynamics of the nonlinear terms in a analytical and
controllable way.
