Nakayama, M.; Mason, D. P. On the existence of compressive solitary waves in compacting media. (English) Zbl 0841.76087 J. Phys. A, Math. Gen. 27, No. 13, 4589-4599 (1994). Summary: Necessary conditions for the existence of compressive solitary-wave solutions which describe the two-phase fluid flow in a medium compacting under gravity are derived. It is shown that for the existence of compressive solitary-wave solutions which satisfy certain boundary conditions it is necessary 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. Cited in 2 Documents MSC: 76T99 Multiphase and multicomponent flows 35Q51 Soliton equations 86A60 Geological problems Keywords:one-dimensional migration of melt through Earth’s mantle; permeability; viscosity PDFBibTeX XMLCite \textit{M. Nakayama} and \textit{D. P. Mason}, J. Phys. A, Math. Gen. 27, No. 13, 4589--4599 (1994; Zbl 0841.76087) Full Text: DOI