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Journal of Applied Mathematics
Volume 2013, Article ID 926512, 8 pages
Research Article

Bifurcation Analysis of a Coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-Type Model

Lei Shi1,2

1School of Sciences, Nanjing Agricultural University, Nanjing 210095, China
2School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210046, China

Received 24 April 2013; Accepted 2 July 2013

Academic Editor: Abdul Hamid Kara

Copyright © 2013 Lei Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the bifurcation and stability of trivial stationary solution of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length of the domain regarded as bifurcation parameter, branches of nontrivial solutions are shown by using the perturbation method. Moreover, local behavior of these branches is studied, and the stability of the bifurcated solutions is analyzed as well.