Abstract
The existence and stability of solitary excitations associated with longitudinal dust grain motion in a dusty plasma crystal [1, 2] is considered in this investigation. The theoretical modelling of this problem has originally relied on a KORTEWEG D E VRIES (KdV) type description [3], which predicted compressive solitary density excitations (only). Not surprisingly, such excitations were experimentally found to exist [4]. A more rigorous recent investigation of dust lattice dynamics, from first principles [5], has shown that the KdV picture, despite its analytical simplicity, appears to be rather incomplete: in specific, it neglects higher(than cubic) order interaction nonlinearity [5]. Our aim here is to revisit the problem of nonlinear longitudinal dynamics in DP crystals and, in fact, to show that rarefactive solitons may also occur in dusty plasma crystals. The discrete equation of longitudinal motion for the «—th dust-grain in a crystal reads:
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