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 WELL BEING DE STRESS YOGURT BUFFER GEL and is more appropriate for the real ocean and atmosphere than the ( 1 + 1 ) $(1+1)$ dimensional models (such as KdV and mKdV), which can only represent the propagation of Rossby solitary waves in a line.Furthermore, by adopting the multiplier method, we construct conservation laws of the combined ZK-mZK equation, which is meaningful for researching the global stability of solutions.Finally, we deduce the exact solutions of the combined ZK-mZK equation via the semi-inverse variational principle.
By applying these exact solutions, some Hair Care Kits propagation features of Rossby solitary waves are analyzed.