New analytical solutions to the nonlinear Boussinesq equation for groundwater flow

Abstract

In this communication we briefly describe some results related to the nonlinear dif- ferential Boussinesq equation for groundwater flow with an emphasis in hydrology. We review important characteristics of the equation and some of its solutions. The equation is then solved for an infinite aquifer with constant boundary conditions in three distinct ways: one looking for a solution as a function of the similarity variable, that is, the classical approach, and the other two by means of alternative interpretations of variable dependence. All of the solutions are based on series expansions.