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Аннотация:Nonlinear equations of the Kadomtsev-Petviashvili type are derived for Alfvén and magnetosonic waves propagating at a small angle to the Earth's magnetic field. This represents a generalization of the derivative nonlinear Schrödinger equation to the two-dimensional case. The theory is applied to explain the observations of stable Alfvén-like solitons by means of the Aureol 3 satellite during the Russian seismic impact experiments. It may also be useful for theoretical interpretations of the chevron structures of the ``pearls'' that are occasionally observed in the Earth's magnetosphere.