On The Bifurcation Of The Equilibrium Solution Of The Kuramoto-Sivashinsky Equation

This paper deals with the bifurcation of Kuramoto-Sivashinsky equation in one dimensional space by Liapunov-Schmidt reduction when the parameter λ goes through the bifurcating point λ_k = k~2 (k = 1,2,…). Here, weprove that the Kuramoto-Sivashinsky equation bifurcates from (u,λ) = (0,λ_k) exactly two equilibrium solutions in odd function space and bifurcates a circle in the whole space, which consists of equilibrium solutions, where λ_k = k~2 (k = 1,2, …).