
 
Approximate Solution of the KuramotoShivashinsky Equation on an Unbounded Domain 
 
Citation： 
Wael W. MOHAMMED.Approximate Solution of the KuramotoShivashinsky Equation on an Unbounded Domain[J].Chinese Annals of Mathematics B,2018,39(1):145~162 
Page view： 362
Net amount： 666 
Authors： 
Wael W. MOHAMMED; 
Foundation： 
This work was supported by the Deanship of Scientific
Research, University of Hail, KSA (No.0150258). 


Abstract： 
The main goal of this paper is to approximate the
KuramotoShivashinsky (KS for short) equation on an unbounded
domain near a change of bifurcation, where a band of dominant
pattern is changing stability. This leads to a slow modulation of
the dominant pattern. Here we consider PDEs with quadratic
nonlinearities and derive rigorously the modulation equation, which
is called the GinzburgLandau (GL for short) equation, for the
amplitudes of the dominating modes. 
Keywords： 
Multiscale analysis, Modulation equation, KuramotoShivashinsky equation,GinzburgLandau equation 
Classification： 
35B20, 35B45, 35B35 

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