Analysis of solitary wave solutions of the ZK equation for magnetized Rossby waves under background shear flow

Abstract

Magnetized Rossby waves are low-frequency planetary waves formed by the coupling of Earth’s rotation and geomagnetic field, and their high-dimensional nonlinear theoretical system remains to be improved. Based on the geomagnetically modified dimensionless Charney equation, combined with multi-scale analysis and perturbation expansion method, this paper derives the (2+1)-dimensional Zakharov–Kuznetsov (ZK) equation for magnetized Rossby waves. The Hirota bilinear method is adopted to solve the ZK equation, and the analytical solutions of 1-soliton, 2‐soliton and 3‐soliton are obtained. Combined with the amplitude distribution and flow field characteristics, the propagation laws and evolution characteristics of solitons are systematically analyzed. Meanwhile, the influence mechanism of background flow intensity and geomagnetically modified generalized Rossby parameter on the dynamic characteristics of solitons is explored. This study further improves the high-dimensional nonlinear theoretical system of magnetized Rossby waves and can provide important theoretical support for ionospheric observation analysis and explanation of nonlinear dynamic mechanisms.