  We prove the existence and uniqueness of a family of travelling waves in a
degenerate (or singular) quasilinear parabolic problem that may be regarded as
a generalization of the semilinear Fisher-Kolmogorov-Petrovski-Piscounov
equation for the advance of advantageous genes in biology. Depending on the
relation between the nonlinear diffusion and the nonsmooth reaction function,
which we quantify precisely, we investigate the shape and asymptotic properties
of travelling waves. Our method is based on comparison results for semilinear
ODEs.
