Solitary-waves in geophysical two-phase viscous media: A semi-analytical solution

► We investigate the migration of two phase viscous flow in geodynamical settings. ► Semi-analytical solitary-wave solution of the two-phase flow equation is given. ► Variation of the effective viscosity with porosity induces a sharpening of waves. ► Increase of background porosity decreases solitary waves speed. ► Our analytical solution can be used to benchmark two-phase numerical model.