F. Calogero et S. Delillo, FLUX INFILTRATION INTO SOILS - ANALYTIC SOLUTIONS, Journal of physics. A, mathematical and general, 27(5), 1994, pp. 137-142
The Burgers model for flux infiltration into a semi-infinite soil is s
olved for generic space-dependent initial moisture and time dependent
supply rate. General formulae in terms of quadratures are obtained for
the moisture content and for the time to ponding of the soil.