We present numerical simulations of wave coupling: in a cold, ideal, i
nhomogeneous plasma waveguide which approximates the flanks of the mag
netosphere. Two types of driving conditions are investigated. The firs
t corresponds to a displacement of the magnetopause over a fixed azimu
thal range. The pulsations driven by this boundary condition have an a
zimuthal wavenumber and phase speed determined by the equilibrium stru
cture of the magnetosphere. The second condition corresponds to a disp
lacement pulse which runs antisunward along the magnetopause and produ
ces pulsations with a phase velocity strictly equal to that of the bou
ndary pulse. Our results are compared briefly with data and suggest th
at on some occasions the magnetosphere is driven in a fashion that is
well approximated by a. ''running'' pulse or wave on the magnetopause.