Bifurcations and pattern formation in the "regularized" Kuramoto-Sivashinsky equation

H. S. Brown*, I. G. Kevrekidis, A. Oron, P. Rosenau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We study the bifurcation patterns of the "regularized" Kuramoto-Sivashinsky equation (RKS), which results from relaxation of the long-wave approximation in the Kuramoto-Sivashinsky equation (KS). Both equations model the flow of a viscous thin film down a vertical plane, and the RKS was recently introduced to model sharp gradient patterns that cannot be captured by the KS. We show that in some flow regimes, relaxation of the long-wave approximation, even without solution breakup, causes a profound effect on the secondary and even on the primary instabilities, which now can become subcritical.

Original languageEnglish
Pages (from-to)299-308
Number of pages10
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number4
StatePublished - 23 Mar 1992
Externally publishedYes


FundersFunder number
Center for Nonlinear Studies
Israel—Mexico Energy Research Fund
National Science FoundationCTS-895721 3, DMS-8906292
David and Lucile Packard Foundation
Los Alamos National Laboratory


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