  Convective counterparts of variants of the nonlinear Fisher equation which
describes reaction diffusion systems in population dynamics are studied with
the help of an analytic prescription and shown to lead to interesting
consequences for the evolution of population densities. The initial value
problem is solved explicitly for some cases and for others it is shown how to
find traveling wave solutions analytically. The effect of adding diffusion to
the convective equations is first studied through exact analysis through a
piecewise linear representation of the nonlinearity. Using an appropriate small
parameter suggested by that analysis, a perturbative treatment is developed to
treat the case in which the convective evolution is augmented by a small amount
of diffusion.
