TY - JOUR

T1 - Bifurcations and pattern formation in the "regularized" Kuramoto-Sivashinsky equation

AU - Brown, H. S.

AU - Kevrekidis, I. G.

AU - Oron, A.

AU - Rosenau, P.

N1 - Funding Information:
We would like to thank Dr. James M. Hyman and Professor Edriss S. Titi for helpful discussions. The work of H.S.B. and I.G.K. was supported in part by NSF Grants CTS-895721 3, DMS-8906292 and a Dvaid and Lucile Packard Foundation Fellowship. A.O. was partially supported by the Israel—Mexico Energy Research Fund. Part of this work was performed while I.G.K. and P.R. were enjoying the hospitality of, and A.O. was supported by, the Center for Nonlinear Studies at Los Alamos National Laboratory.

PY - 1992/3/23

Y1 - 1992/3/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0342885418&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(92)91016-K

DO - 10.1016/0375-9601(92)91016-K

M3 - מאמר

AN - SCOPUS:0342885418

VL - 163

SP - 299

EP - 308

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 4

ER -