The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems

Details The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems The Swift-Hohenberg Equation Requires Non-Local Modifications to Model Spatial Pattern Evolution of Physical Problems

1994-12-09

arxiv.org/abs/patt-sol/9412002v1

Nonlinear Sciences

Pattern Formation and Solitons

7 pages, standard LaTeX (without figures), 18K

Scientific paper

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.

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