Traveling wave solutions of saturated‐unsaturated flow through porous media

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Abstract
Traveling wave solutions to the problem of saturated‐unsaturated flow of water through a uniform porous medium are derived, and the regularity properties of the solutions are studied. It is found that a singularity occurs in the higher‐order derivatives of flux with respect to the space coordinate in the solutions at water tables and that the water tables can be generally interpreted as propagating acceleration waves of the nth order, where n is a positive integer.