1994/12/09 by A. J. Roberts, Roberts, A. J.
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Theoretical and Computational Physics #nlin.PS #patt-sol
paper · pdf · doi:10.48550/arxiv.patt-sol/9412002
7 pages, standard LaTeX (without figures), 18K
arxiv created 1994/12/09 · openalex publication_date 1994/12/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.