Abstract
In this paper we have considered the $$(2+1)$$ filtration-absorption equation that models the flow of impure water in a water-absorbing fissured porous medium. We have applied the Lie method to get the Lie symmetries classification with respect to the parameter of the equation and we have interpreted them. Additionally, we have obtained solutions for the travelling wave case. Lastly, all low-order conservation laws have been obtained by using the direct method of multipliers. Its associated conserved integral is also interpreted.
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