Modulation instability of the nonlinear Alfven waves

Modulation instability of the nonlinear Alfven waves in the high-temperature plasma βe≅β1≅1 taking into account resonance particles is discussed. The dispersion equation for the longitudinal disturbances and the instability increments in the regions κ<<κ*0, κ>>κ*0, κ∼κ*0. For short wave disturbances κ>>κ*0 the dispersion equation leads to the known formula for Landau coefficient of nonlinear damping. As an example of an application of the formula obtained the correlation and crosscorrelation functions of disturbances of the magnetic field longitudinal components of the Alfven waves, spreading along the magnetic field are calculated