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 limi ting cases according to whether the dusty cylinder radius is larger or smal ler than the plasma Debye length. Spatial restrictions of a dusty plasma le ad to an increase in the dispersion in the long wavelength limit, to substa ntial modifications of the longitudinal modulational instability and to the possible formation of nonlinear Schrodinger type solitons. In both cases t here is a threshold for solitary wave formation.