Volume 72, Number 6, December 2005
|Page(s)||894 - 900|
|Published online||16 November 2005|
Weakly vs. highly nonlinear dynamics in 1D systems
CNRS/Laboratoire de Spectrométrie Physique, Université Joseph Fourier Grenoble 1 BP 87, F-38402 St Martin d'Hères, France
Accepted: 19 October 2005
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.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 47.54.+r – Pattern selection; pattern formation
© EDP Sciences, 2005
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