Weakly versus highly nonlinear dynamics in 1D systems

Abstract

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.

to be published in Europhys. Lett