A caravan of fast ships in a wide rough canal

It is known that when a boat advances near critical speed in a wide canal, solitons can be radiated upstream in a transient manner.  Real canals are not flat, therefore we considered a canal with a randomly rough bed. Governing equations were shown to be in the form of forced-damped KdV equation and numerical evaluations showed less transient behavior in forces and moments. However, striking results emerged when we considered an array of ships advancing in the canal. When a caravan of ships moves over a flat (with no bathymetry undulation) canal, bow and stern waves unsteadily interact resulting in irregular and extreme forces and moments from time to time. But surprisingly, if roughness is taken into account and in a relatively short transient time, the bow wave of a front ship upon encountering and interacting with the stern wave of a back ship forms a smooth steady pattern: another miracle of nonlinear equations.