Periodic boundary conditions for KdV-Burgers equation on an interval

For the KdV-Burgers equation on a finite interval the development of a regular profile starting from a constant one under a periodic perturbation on the boundary is studied. The equation describes a medium which is both dissipative and dispersive. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (similarly to the Burgers equation case). But due to dispersion each such front is followed by increasing oscillation leading to the next shock-like the ninth wave in rough seas. The development of such a profile is preceded by an initial shock of a constant height.