  The weakly nonlinear regime of transverse paramagnetic dust grain
oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity,
which is related to the sheath electric/magnetic field(s) and to the
inter--grain (electrostatic/magnetic dipole) interactions, is shown to lead to
the generation of phase harmonics and, in the case of propagating transverse
dust-lattice modes, to the modulational instability of the carrier wave due to
self--interaction. The stability profile depends explicitly on the form of the
electric and magnetic fields in the plasma sheath. The long term evolution of
the modulated wave packet, which is described by a nonlinear
Schr\"odinger--type equation (NLSE), may lead to propagating localized envelope
structures whose exact forms are presented and discussed. Explicit suggestions
for experimental investigations are put forward.
