Kuramoto–Sivashinsky equation boundary-value problem stability bifurcation invariant manifolds
Issue Date:
2015
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 25, No 1, (2015), 81p-90p
Abstract:
Kuramoto–Sivashinsky equation with periodic boundary-value conditions is considered. The stability of the homogeneous equilibrium is investigated as well as the local bifurcation of the spatially nonhomogeneous t-periodic solutions. It is shown that the two-dimensional invariant manifolds are composed of these solutions. These manifolds can be stable or unstable, but all
solutions belonging to these manifolds are always unstable. The bifurcation problem can be reduced to investigate certain system of
ordinary differential equations (normal form). This normal form was constructed by a modified Krylov–Bogolubov algorithm. These normal forms can be used to explain a ripple topography induced by ion bombardment. 2010 Mathematics Subject Classification: 35K35, 35B32.
