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The propagation of dust-lattice waves in two-dimensional hexagonal dusty plasma crystals in the presence of an external weak magnetic field is considered. Linear and nonlinear properties of the longitudinal dust-lattice waves are investigated. Dispersion relation, group velocity and evolution equation are found. The influence of the magnetic field on the propagation of dust-lattice waves is studied. We obtain the envelope evolution equation for longitudinal modes in the presence of a weak magnetic field, which is in the form of the Gross–Pitaevskii equation.
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Shahmansouri et al. (2012) studied this question.
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