English

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.

Keywords

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

R2 v1 2026-07-22T18:47:24.502Z