It is shown that in the earth's conductive ionospheric E-region, large-scale ultra low-frequency Rossby and Khantadze electromagnetic waves can propagate. Along with the prevalent effect of Hall conductivity for these waves, the latitudinal inhomogeneity of both the earth's angular velocity and the geomagnetic field becomes essential. Action of these effects leads to the coupled propagation of electromagnetic Rossby and Khantadze modes. Linear propagation properties of these waves are given in detail. It is shown that the waves lose the dispersing property for large values of wave numbers. Corresponding nonlinear solitary vortical structures are constructed. Conditions for such self-organization are given. It is shown that nonlinear large-scale vortices generate the stronger pulses of the geomagnetic field than the corresponding linear waves. Previous investigations are revised.