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

Abstract

We study the bifurcation and stability of trivial stationary solution $(\mathrm{0},\mathrm{0})$ of coupled Kuramoto-Sivashinsky- and Ginzburg-Landau-type equations (KS-GL) on a bounded domain $(\mathrm{0},L)$ with Neumann's boundary conditions. The asymptotic behavior of the trivial solution of the equations is considered. With the length $L$ 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.