Nonlinear waves in hot magnetized plasma

Nonlinear low-frequency long wavelength waves are studied in the framework of the proposed method of the direct kinetic equation expansion in the inverse gyrofrequency power series. Nonlinear two-dimensional equations are found for perpendicular magnetosonic waves with subsequent reduction to the Korteweg-de Vries equation for quasistationary one-dimensional (QS1D) perpendicular magnetosonic wave. The dispersion is determined by the ion gyroradius ρ_i Equations for nonlinear QS1D parallel Alfvén waves and QS1D oblique fast magnetosonic waves are found. It is shown that the form of the equations coincides with that one obtained from hydrodynamics but the dispersion lengths and coefficients at nonlinear terms are different. Dispersion of quasiparallel fast waves is positive and determined by the ion inertial length c/ω_pi, while quasiperpendicular waves have negative dispersion determined by the ion gyroradius ρ_i.