Nonlinear equations of the Kadomtsev-Petviashvili type are derived for
Alfven and magnetosonic waves propagating at a small angle to the Ear
th's magnetic field. This represents a generalization of the derivativ
e nonlinear Schrodinger equation to the two-dimensional case. The theo
ry is applied to explain the observations of stable Alfven-like solito
ns by means of the Aureol 3 satellite during the Russian seismic impac
t experiments. It may also be useful for theoretical interpretations o
f the chevron structures of the ''pearls'' that are occasionally obser
ved in the Earth's magnetosphere.