ON THE EXISTENCE OF COMPRESSIVE SOLITARY WAVES IN COMPACTING MEDIA

Necessary conditions for the existence of compressive solitary-wave so lutions of a partial differential equation derived by Scott and Steven son which describes the two-phase fluid flow in a medium compacting un der gravity are derived. It is shown that for compressive solitary-wav e solutions to exist which satisfy certain boundary conditions it is n ecessary that n = m > 1 where n and m are the exponents in power laws relating the permeability of the medium and the viscosity of the solid matrix, respectively, to the voidage. The effect of the value of the exponents n and m on the shape of the solitary wave is investigated by using existing analytical solutions and new numerical solutions.