Nonlinear solitary wave in the ionospheric E-region

A nonlinear wave equation for a solitary one-dimensional inhomogeneity is studied. It is similar to the diffusion equation with the diffusion coefficient depending on the phase velocity. The phase velocity depends, in turn, on the electron density. A weak inhomogeneity moves with the velocity close to that of the electric drift. If this velocity exceeds the ion acoustic speed the effective diffusion is negative, and the inhomogeneity grows and contracts. The velocity of the growing inhomogeneity becomes smaller. It absorbs weaker and faster moving inhomogeneities from the back side. In a stationary regime, the ionosphere will be filled with rare but strong inhomogeneities with sharp back sides.