It is shown that sheared Rossby–Khantadze waves can propagate due to inhomogeneities, taking into account the Earth's angular velocity and the magnetic field. Along with the Hall conductivity, these waves can couple in the ionospheric E region.The novelty of the present work is the consideration of magnetic field inhomogeneity, which was not considered before and reduced our considered system of equations to a 1D modified KdV equation.