A generalized analytical solution for a nonlinear infiltration equation using the exp-function method

The infiltration problem is one of the most interesting issues considered by geotechnical and water engineers. Many researchers have studied the infiltration problem and have developed models that can be categorized by analytical and numerical concepts. For nonlinear infiltration simulation, however, analytical solutions are few due to the difficulties and complexities involved. The Richards equation is one of the most well-known equations to describe the behavior of unsaturated infiltration zones in soil; many other relations have been introduced based on this equation. The exp-function method is one of the most recent analytical approaches used for the solution of nonlinear Partial Differential (or algebraic) Equations (PDE). In this paper, the exp-function method, with the aid of symbolic computation systems, in particular Maple, has been applied to the Richards equation to evaluate its effectiveness and reliability, and to reach a more generalized solution of the problem. Free parameters can be determined using initial or boundary conditions and the soil water content at any given time and depth is determined in a semi-infinite and unsaturated porous medium. It is shown that the exp-function method applied here results in a more realistic solution and that the concept is very effective and convenient.