Exact Solutions of the Groundwater Filtration Equation via Dynamics

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Sinian Tao


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.


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Tao, S. (2024). Exact Solutions of the Groundwater Filtration Equation via Dynamics. Advances in Systems Science and Applications, 24(1), 163-168. https://doi.org/10.25728/assa.2024.24.1.1604