Nonlinear low-frequency modes in a cylindrical dusty plasma waveguide

The propagation of nonlinear low-frequency waves in a dusty plasma cylinder along its axis is investigated. Nonlinear waves are considered in two limiting cases according to whether the dusty cylinder radius is larger or smaller than the plasma Debye length. Spatial restrictions of a dusty plasma lead to an increase in the dispersion in the long wavelength limit, to substantial modifications of the longitudinal modulational instability and to the possible formation of nonlinear Schrodinger type solitons. In both cases there is a threshold for solitary wave formation.