Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation

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理论物理通讯 ›› 2011, Vol. 55 ›› Issue (04) : 685-687.

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Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation

HUANG Qiong-Wei and TANG Jia-Shi

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Abstract

Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure. The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfok bifurcation to produce two asymptotically stable solutions. Furthermore, when the distance from bifurcation is of comparable order ε²(|ε|<< 1), the first two terms in ε-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method. Such information is useful to the bifurcation control.

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HUANG Qiong-Wei and TANG Jia-Shi. Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation[J]. 理论物理通讯, 2011, 55(04): 685-687

HUANG Qiong-Wei and TANG Jia-Shi. Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation[J]. Communications in Theoretical Physics, 2011, 55(04): 685-687

中图分类号： 47.20.Ky 46.15.Ff 04.25.Nx