A comprehensive analytical theory for nonlinear excitations related to
horizontal (longitudinal, acoustic mode) as well as vertical (transverse,
optical mode) motion of charged dust grains in a dust crystal is presented.
Different types of localized excitations, similar to those well known in solid
state physics, are reviewed and conditions for their occurrence and
characteristics in dusty plasma crystals are discussed. By employing a
continuum approximation (i.e. assuming a long variation scale, with respect to
the inter-particle distance) a dust crystal is shown to support nonlinear
kink-shaped supersonic solitary excitations, associated with longitudinal dust
grain displacement, as well as modulated envelope localized modes associated
with either longitudinal or transverse oscillations. Although a one-dimensional
crystal is considered for simplicity, the results in principle apply to a
two-dimensional lattice if certain conditions are satisfied. The effect of
mode-coupling is also briefly considered. The relation to previous results on
atomic chains, and also to experimental results on strongly-coupled dust layers
in gas discharge plasmas, is briefly discussed.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004,
Nice (France
