Abstract In the present paper. a new partial differential equation has been obtained to describe the Rossby solitary waves with complete Coriolis force by employing multi-scale analysis and perturbation method. we call it combined ZK-mZK equation. The equation can reflect the propagation of Rossby waves on the plane and is more appropriate for the real ocean and atmosphere than the ( ... https://bbmbatteryes.shop/product-category/1139/