Analytical solution of one-dimensional transient phreatic flow and its application

The symmetry of the 1-D Boussinseq equation for transient phreatic flows is discussed in this paper.And its analytical solution under such conditions as initial and boundary conditions is obtained by the method of the Lie group transformation.The errors between the non-linear Boussinesq equation and that of its linearization are compared.Based on the analytical solution,a new method for null error linearization of the Boussinesq equation is proposed,and some principles in the linearization are analyzed.