Peculiarities of the evolution dynamics of strong MHD disturbance in the magnetosphere are investigated. Transformation of the Alfven wave into the fast and slow magnetosound waves at collision of contrary impulses, which is taking place along the Earth magnetic field, is considered. The dependence of effects on angle declination of the Alfven wave to the magnetic field and on ratio of sound velocity to Alfven velocity in plasma are analysed. Nonlinear transformation of the Alfven waves in the magnetosounds ones at reflection of the Alfven wave from the walls of magnetospheric resonator at various angles of the Earth magnetic field in a point of reflection is considered in this article as well. Special attention is paid to effects, which role increase with decrease of temperature and sound velocity in plasma. The analytical evaluations matched with considered effects in case of average nonlinearity are made, and peculiarities to approach of cold plasma are also studied. The role of the Earth ionosphere-atmosphere space in these phenomena is investigated. It is marked, that isolated strong Alfven wave can induce the essential plasma concentration redistribution in the Earth ionosphere. The dependence of this effect on ratio of Alfven velocity to sound one is considered. 
Two kinds of nonstabilities, arising in the nonlinear MHD equations, are detected. The role of dissipative viscosity parameters for maintenance of the stable numerical account is shown.