  Intrinsic Localized Modes (ILM) (or Discrete Breathers, DB) are localized
oscillatory modes known to occur in atomic or molecular chains characterized by
coupling and/or on-site potential nonlinearity. Quasi-crystals of charged
mesoscopic dust grains (dust lattices), which have been observed since hardly a
decade ago, are an exciting paradigm of such a nonlinear chain. In
gas-discharge experiments, these crystals are subject to forces due to an
externally imposed electric and/or magnetic field(s), which balance(s) gravity
at the levitated equilibrium position, as well as to electrostatic inter-grain
interaction forces. Despite the profound role of nonlinearity, which may be due
to inter-grain coupling, mode- coupling and to the sheath environment, the
elucidation of the nonlinear mechanisms governing dust crystals is still in a
preliminary stage. This study is devoted to an investigation, from very first
principles, of the existence of discrete localized modes in dust layers.
Relying on a set of evolution equation for transverse charged grain
displacements, we examine the conditions for the existence and sustainance of
discrete localized modes and discuss the dependence of their characteristics on
intrinsic plasma parameters. In addition, the possibility of DB stabilisation
via an external force is discussed.
