Solitary and breather dynamics of Rossby–Khantadze waves in the ionospheric E-region: a Kadomtsev–Petviashvili study

Abstract

This study focuses on the weakly ionized E-region of the ionosphere. It systematically investigates (2+1)-dimensional nonlinear Rossby–Khantadze (RK) waves, considering the effects of the Earth’s rotational angular velocity and the latitudinal inhomogeneity of the geomagnetic field. Starting from the potential vorticity equation, this study adopts multi-scale analysis and weakly nonlinear perturbation expansion to derive the Kadomtsev–Petviashvili (KP) equation. To explore the nonlinear evolution of RK waves, the KP equation is solved using the Hirota bilinear method. This yields one-, two-, three-, and N-soliton solutions together with breather-type traveling wave solution. Amplitude and flow field evolution diagrams are generated for each solution. These diagrams provide intuitive support for analyzing the evolutionary characteristics of RK waves. This study also investigates the effects of two key factors on RK waves: the intensity of background shear flow and the intensity of latitudinal inhomogeneity in the background geomagnetic field (characterized by the z-component gradient). The results indicate that changing either factor significantly alters the propagation velocity and amplitude of RK solitary waves. For breather-type RK traveling waves, moderate variations in these two factors affect their maximum amplitude and propagation velocity during propagation. However, they do not alter the periodic evolutionary characteristics of these waves.