  We analyze the morphological transition of a one-dimensional system described
by a scalar field, where a flat state looses its stability. This scalar field
may for example account for the position of a crystal growth front, an order
parameter, or a concentration profile. We show that two types of dynamics occur
around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics.
The conditions under which highly nonlinear evolution equations appear are
determined, and their generic form is derived. Finally, examples are discussed.
