In barotropic fluids, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous nonlinear Schrdinger equation including topographic forcing and an external source is derived by employing the perturbation method and stretching transforms of time and space. With the inspection of the evolution of the amplitude of Rossby envelope solitary waves, it is found that effect, topography effect and an external source are the important factors, the solitary Rossby wave is induced though the basic stream function has a shear flow. On the assumption that nonlinear and topographic effects are balanced, an inhomogeneous equation is derived, and the results show that the topography and Rossby waves interact in the barotropic flow. The inhomogeneous nonlinear Schrdinger equation describing the evolution of the amplitude of solitary Rossby envelope solitary waves as the change of Rossby parameter (y) with latitude y, topographic forcing and the external source is obtained.