Exact solutions to the nonlinear Rossby waves with a complete representation of the Coriolis force

A horizontal component of the earth's rotation is included in a set of Boussinesq fluid equations, which have a constant horizontal component of the Coriolis parameter, while the vertical component varies with latitude. The nonlinear Rossby waves described by the KdV equation are derived. Its periodic-wave and soliton solution are also obtained. The results show that the f(H) = 2 Omega cos phi effect can be important if the perturbations are functions of the latitude. We also find that when the perturbations are independent of latitude, the f(H) effect disappears.