We present a full-scale simulation of the nonlinear interaction between an intense electromagnetic wave and the Earth's ionosphere, by means of a generalized Zakharov model. The radio wave propagates from the neutral atmosphere into the ionospheric plasma layer and reaches the turning points of the ordinary and extraordinary wave modes. At the turning point of the ordinary mode, a parametric instability takes place in which the electromagnetic wave decays into an electron plasma wave and an ion acoustic wave with a typical wavelength of one meter. This is followed by collapse and caviton formation and trapping of the intense electron plasma wave. The cavitons lead to an efficient excitation of slow X (or Z) waves that propagate further into the denser ionospheric layer at higher altitudes. We use a realistic ion (oxygen) mass, length scales, and other plasma parameters. This numerical study should be useful for understanding the nonlinear interaction between intense radio waves and the ionosphere.