Localized excitations in dusty plasma crystals: A survey of theoretical results

The nonlinear aspects of dust motion in one- (1D) and two-dimensional (2D) dust lattices are reviewed. Horizontal (longitudinal, acoustic) as well as vertical (transverse, optic-like) dust grain motion in 1D monolayer is studied. Dust crystals are shown to support nonlinear kink-shaped solitary excitations (density solitons), related to longitudinal (in-plane) dust grain displacement, as well as modulated envelope localized modes associated with either longitudinal (in-plane, acoustic) or transverse (off-plane, inverse-optic) oscillations. Highly localized excitations ("Discrete Breathers"), associated with transverse dust-grain motion in 1D dust crystals, may also exist, as recently shown from first principles. Hexagonal (2D) dust lattices sustain modulated envelope structures, formed via modulational instability of in-plane vibrations. Discrete analysis of hexagonal crystals also suggests the occurrence of ultra-localized modes and vortices. With the exception of longitudinal density solitons, the above theoretical predictions have not yet been tested in the laboratory. This provides a challenging test-bed for experimental investigations, which will hopefully confirm these results.