Approximate solutions of the Kuramoto-Sivashinsky equation for periodic boundary value problems and chaos (Q5950579)

The authors develop an approach to find approximate solutions of the Kuramoto-Sivashinsky (KS) equation for boundary value problems (BVPs). Attention is focused to BVP with periodic boundary conditions. This approach is used to find the approximate solution for stress-free and rigid boundary condition. The solution of the KS equation for BVPs in finite domains exhibits spatio-temporal chaos. They show that the solutions of the KS equation exhibit chaos and their time average pattern regularize for large time. But it becomes asymptotically regular.