Abstract
The existence and stability of solitary excitations associated with longitudinal dust grain motion in a dust lattice is considered. A detailed investigation of dust lattice dynamics, from first principles, has shown that the KdV picture appears to be rather incomplete: in specific, it neglects higher- (than cubic) order interaction nonlinearity. Advancing to a fourth-order theory, it is shown that longitudinal dust lattice is modelled by an extended KdV (eKdV) equation or by a Boussinesq type equation. Results thus obtained suggest that both rarefactive and compressional excitations are possible and exact expressions for their physical characteristics (amplitude, width) are obtained. The validity of this improved approach is established by checking that the quartic nonlinearity coefficient is of comparable magnitude to its cubic counterpart and may therefore not be neglected. These results complemented the physical parameters involved in a nonlinear lattice-dynamical description are modified if one takes into account interaction polarization (dressing) effects. A change in sign is also possible thus leading to a structural change in the excitations occurring in the crystal. Rarefactive or compressive longitudinal dust lattice excitations may occur in a dust crystal.
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