Bifurcation diagram of stationary solutions of the 2D Kuramoto-Sivashinsky equation in periodic domains.

Abstract

Abstract The solution tree of the 2D stationary Kuramoto-Sivashinsky equations in the periodic domain is analized using the analytical and numerical methods. The evolution of stationary solutions is considered by constructing the bifurcation diagram. Some bifurcation points on the main solution are found analytically, where secondary bifurcations are analized numerically. The bifurcation diagram is constructed using the deflated pseudo arc-length continuation process that allows one to find both connected and disconnected branches of solutions. The resulting bifurcation diagram is analized and subdivided according to characteristic properties of the solution. Different solution branches are visualized in the physical space.