Simplified asymptotic equations are developed for the nonlinear interaction of long wavelength equatorial Rossby waves and barotropic Rossby waves with a significant midlatitude projection in the presence of suitable horizontally and vertically sheared zonal mean flows. The simplified equations allow for nonlinear energy exchange between barotropic Rossby waves and the baroclinic equatorial waves. Idealized examples in the model demonstrate that midlatitude Rossby wave trains can transfer energy to localized equatorially trapped baroclinic Rossby waves thorugh a nonlinear "westerly wind burst" mechanism. Conversely, equatorially trapped baroclinic Rossby wave trains in the idealized model can transfer substantial energy to the midlatitude barotropic Rossby waves. The role of frictional drag on these waves will also be treated. From the view point of applied mathematics, the asymptotic equations derived here are a novel set of nonlinear wave-wave-mean flow equations.