  The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic
(R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the
inertialess electron equation of motion, inertial ion equation of motion,
Amp\`ere's law, Faraday's law, and the continuity equation in a plasma with
immobile charged dust grains, the linear and nonlinear propagation of
two-dimensional R-D-MHD waves are investigated. In the linear regime, the
existence of immobile dust grains produces the Rao cutoff frequency, which is
proportional to the dust charge density and the ion gyrofrequency. On the other
hand, the dynamics of an amplitude modulated R-D-MHD waves is governed by the
cubic nonlinear Schroedinger equation. The latter has been derived by using the
reductive perturbation technique and the two-timescale analysis which accounts
for the harmonic generation nonlinearity in plasmas. The stability of the
modulated wave envelope against non-resonant perturbations is studied. Finally,
the possibility of localized envelope excitations is discussed.
