Variable coefficient KdV system for the non-linear Rossby waves

The paper deals with a non-linear barotropic vorticity equation in a shear flow, the model is applied to get the non-linear Rossby solitary wave with the effects of topography and other external forcing. Basing on the perturbation method, the variable coefficient KdV equation is derived for Rossby waves. The periodic-like solution for the equation is obtained with the help of Jacobi elliptic functions, the solitary solutions can also be obtained in the limit case. The analysis indicates that the wave amplitude and velocity will be related to the topography effect. It is also shown that the external forcing plays an important role in evolution of the waves.