For the weakly ionized E layer plasma, a generalized Charney-Obukhov equation for magnetized Rossby waves is derived. This magnetized Rossby wave is produced by the dynamo electric field and represents the ionospheric generalization of tropospheric Rossby waves in a rotating atmosphere by the spatially inhomogeneous geomagnetic field. The basic characteristics of the wave are given. The modified Rossby velocity and Rossby-Obukhov radius are introduced. The mechanism of self-organization into solitary vortical nonlinear structures is examined. The mechanism of a self-organization of solitary structures is the result of the mutual compensation of wave dispersion and interaction through the scalar and Poisson bracket convective nonlinearities in the nonlinear wave equation. As a result, the solitary structures are anisotropic, containing a circular vortex superimposed on a dipole perturbation. The degree of anisotropy sharply increases when the vortex size approaches the so-called intermediate geostrophic size.