The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems
patt-sol
2008-02-03 v1 Pattern Formation and Solitons
Abstract
I argue that ``good'' mathematical models of spatio-temporal dynamics in two-dimensions require non-local operators in the nonlinear terms. Consequently, the often used Swift-Hohenberg equation requires modification as it is purely local. My aim here is to provoke more critical examination of the rationale for using the Swift-Hohenberg equations as a reliable model of the spatial pattern evolution in specific physical systems.
Cite
@article{arxiv.patt-sol/9412002,
title = {The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems},
author = {A. J. Roberts},
journal= {arXiv preprint arXiv:patt-sol/9412002},
year = {2008}
}
Comments
7 pages, standard LaTeX (without figures), 18K