Abstract: Movement of magma through the earth’s mantle can be seen as porous media flow. To model this molten rock migration we derive a model describing a viscous fluid flow through a compacting solid matrix based on work by McKenzie. Upon simplification using, inter alia, a Boussinesq approximation we arrive at a more tractable non-linear model with rich behaviour. Solitary wave type solutions have been observed numerically for simplified models in literature and analytic expressions for a restricted class of travelling waves are derived which confirm the existence of these special waves. Strong evidence to date suggests that these special wave solutions are not solitons.