Depinning transition of a pattern forming system in a washboard potential

We investigate numerically the depinning transition of the Kuramoto-Sivashinsky equation in a washboard potential in one dimension, and find three distinct behaviors. For a certain range of parameters, the transition is well described by the mean field exponent of 1∕2. The next case is that the critical behavior is dominated by the growth of spatially periodic mode with critical exponent 1. Finally, a parameter range exists in which intermittent movement is observed. “Anchor,” which is a spontaneously generated coherent structure, acts as a pinning center. The destruction of anchor is shown to involve a topological change of “unknotting.”