Structure of nonlinear equations of a magnetized plasma and the problem of stability of magnetoacoustic solitons

The problem of generalization of the nonlinear Kortweg-de Vries equation for weakly djspersive waves in a magnetized plasma is discussed. A three-dimensional nonlinear equation for magnetoacoustic waves in such plasmas is derived. It is shown that for waves with frequencies of the order or higher than the ion cyclotron frequency, the structure of the equation differs significantly from that of the three-dimensional Kadomtsey-Petviashvili equation. The three-dimensional stability of one- and two-dimensional magnetoacoustic solitons is investigated. It is shown that two-dimensional magnetoacoustic solitons are stable with respect to longwave three-dimensional perturbations