  For the KdV-Burgers equations for cylindrical and spherical waves the
development of a regular profile starting from an equilibrium under a periodic
perturbation at 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 (sawtooth waves). The development
of such a profile is preceded by a head shock of a constant height and equal
velocity which depends on spatial dimension as well as on integral
characteristics of boundary condition; an explicit asymptotic for this head
shock is found.
