(2+1) dimensional Rossby waves with complete Coriolis force and its solution by homotopy perturbation method

In this paper, the effects of both complete Coriolis force and dissipation on equatorial nonlinear Rossby wave are investigated analytically. From the quasi-geostrophic potential vorticity equation, by using methods of multiple scales and perturbation expansions, a ( 2 + 1 ) dimensional nonlinear Zakharov–Kuznetsov–Burgers equation is derived in describing the evolution of Rossby wave amplitude. The effects of generalized beta, the horizontal component of Coriolis parameter and the dissipation are presented from the Zakharov–Kuznetsov–Burgers equation. We also obtain the classical solitary solution of the Zakharov–Kuznetsov equation when the dissipation is absent by elliptic function expansion method, and the complete Coriolis force effect can be seen by the solution. But the method is failed to Zakharov–Kuznetsov-Burgers equation, therefore, we use the efficient homotopy perturbation method to solve the Zakharov–Kuznetsov–Burgers equation.