The dynamics of a magnetic field in a plasma with dominant Hall effect is e
xamined. The evolution of B in the problem is under the essential influence
of the fluctuations in plasma density generated by del B-2. Solutions of t
wo self-consistent EMHD problems are obtained. It turns out to be possible
to obtain analytical results with the, use of small parameters. The phenome
na described here include self-similar nonlinear waves and the escape of a
small-amplitude precursor from a convective wave.