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Weakly versus highly nonlinear dynamics in 1D systems

O. Pierre-Louis
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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.

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O. Pierre-Louis. 2005-10-20. Weakly versus highly nonlinear dynamics in 1D systems. https://doi.org/10.1209/epl%2Fi2005-10333-6

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