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. (C) 2016 Elsevier B.V. All rights reserved.