Exact Solutions of the Generalized Richards Equation with Power-Law Nonlinearities

We consider a generalized Richards equation with power-law nonlinearities modeling filtration in porous media. Conditions are derived under which the problem can be reduced to the linear heat equation or to nonlinear equations with known solutions. The families of explicit exact solutions that can be expressed via elementary functions or Lambert’s -function are found. Some examples illustrating the results are given.