Modulational instabilities in two-dimensional magnetized dust-lattice

The transverse oscillations of paramagnetic dust grains in hexagonal dusty plasma crystal are discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the weak inter grain interactions (magnetic dipole), is shown to lead to the generation of phase harmonics. In the case of propagating two-dimensional transverse dust-lattice modes in an arbitrary direction, it is shown the modulational instability of the carrier wave is due to self-interaction. The stability depends on the form of the electric field, the magnetic field, and the magnetic permeability of dust particles. The long term evolution of the modulated wave packet is described by a discrete nonlinear Schrodinger equation and it is solved numerically by Adomian decomposition method.