We present numerical simulations of wave coupling in a cold, ideal, inhomogeneous plasma waveguide which approximates the flanks of the magnetosphere. Two types of driving conditions are investigated. The first corresponds to a displacement of the magnetopause over a fixed azimuthal range. The pulsations driven by this boundary condition have an azimuthal wavenumber and phase speed determined by the equilibrium structure of the magnetosphere. The second condition corresponds to a displacement pulse which runs antisunward along the magnetopause and produces pulsations with a phase velocity strictly equal to that of the boundary pulse. Our results are compared briefly with data and suggest that on some occasions the magnetosphere is driven in a fashion that is well approximated by a ''running'' pulse or wave on the magnetopause. ¿ American Geophysical Union 1995