Exact Solutions of the Groundwater Filtration Equation via Dynamics

Abstract

The paper is devoted to the application of finite dimensional dynamics of evolutionary partial differential equations to the Boussinesq filtration equation. The Boussinesq equation is a second order nonlinear equation with three independent variables: time and two spatial coordinates. It describes a shape of the groundwater free surface as it flows through a porous medium under the influence of gravity. This paper proposes a method for constructing exact solutions of the equation, based on the method of finite dimensional dynamics. An example of the evolution of the free surface of groundwater is given.