A new combined ZK-mZK dynamic model for Rossby solitary wave

In this article, using multi-scale and perturbation methods, a partial differential model of Rossby solitary waves with complete Coriolis force effect is obtained, which is called the combined ZK-mZK equation. This equation can reflect the prop?agation characteristics of Rossby waves in space, and is more suitable for real oceans and atmosphere than the (1+1)-dimensional model. According to the pa?rameter composition of the new model, it can be seen that the effect of the complete Coriolis force affects not only the longitudinal structure of the model, but also the amplitude structure of the non-linear long wave.