Steady solutions of the Kuramoto-Sivashinsky equation (Q1082548)

Steady solutions of the Kuramoto-Sivashinsky equation are studied. These solutions are defined on the whole x line and propagate with a constant speed \(c^ 2\) in time. For large \(c^ 2\) it is shown that the solution is unique and has a conical form. For small \(c^ 2\) there is a periodic solution and an infinite set of quasi-periodic solutions as asserted by Moser's twist map theorem. Numerical computations for intermediate values of \(c^ 2\) suggests that below \(c^ 2\approx 1.6\) for every speed there is a continuum of odd quasi-periodic solutions or a Cantor set of chaotic solutions wrapped by infinite sequences of conic solutions.