APPROXIMATE ANALYTICAL SOLUTION OF THE NONLINEAR DIFFUSION EQUATION FOR ARBITRARY BOUNDARY-CONDITIONS

A general approximation for the solution of the one-dimensional nonlin ear diffusion equation is presented. It applies to arbitrary soil prop erties and boundary conditions. The approximation becomes more accurat e when the soil-water diffusivity approaches a delta function, yet the result is still very accurate for constant diffusivity suggesting tha t the present formulation is a reliable one. Three examples are given where the method is applied, for a constant water content at the surfa ce, when a saturated zone exists and for a time-dependent surface flux .