Dynamic water potential waves in unsaturated soils

•The Richards equation is generalized in a systematic way to account for non-diffusive mechanisms giving rise to oscillatory behavior in the water content and total water potential.•The new partial differential equation becomes equivalent to the Richards equation when non-diffusive mechanisms can be neglected, but when this condition is not met, the governing equation describes damped propagating wave behavior of the total water potential.•For a rigid, homogeneous unsaturated soil, the new equation reduces to the telegraph equation, which gives rise to natural time and length scales characteristic of total water potential waves.