  An analytical solution of the nonlinear Richards equation is presented, for
one-dimensional infiltration into a soil of uniform initial moisture content
subject to a constant depth of surface ponded water. Adopted mathematical forms
of the soil water diffusivity and conductivity are flexible enough to model a
range of real soils. The solution takes the form of a power series in $\sqrt
t$, but is observed to converge not only for small times but also for
relatively large times at which travelling-wave-like behavior is evident. The
solution is used to tabulate exact infiltration coefficients with higher-order
corrections as the natural nonlinear limit of soil properties is approached.
Previously published approximate solutions that apply for a wide range of soil
properties are tested against the exact solution and found to be sufficiently
accurate.
