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

An approach to find approximate solutions of the Kuramoto-Sivashinsky (KS) equation for boundary value problems (BVP) is developed. Attention is focus ed to periodic boundary value problems. This approach is used to find the a pproximate solutions for stress-free and rigid boundary conditions. In the first case, it is shown that the spatial pattern of the solutions fluctuate s chaotically for small limes. But it becomes asymptotically regular. The t ime-averaged solutions are also regular. In contrast, the solution for rigi d boundary conditions exhibit robust chaos. (C) 2001 Published by Elsevier Science Ltd.