Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation

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 pitchfork bifurcation to produce two asymptotically stable solutions. Furthermore, when the distance from bifurcation is of comparable order epsilon(2)(vertical bar epsilon vertical bar << 1), the first two terms in epsilon-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method. Such information is useful to the bifurcation control.