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ABSTRACT

The properties of nonlinear dust-acoustic waves in an unmagnetized

collisionless four-component dusty plasma system consisting of electrons,

nonthermal ions, hot and cold dust species have been investigated. The basic

set of fluid equations is reduced to a nonlinear Schrödinger equation via the

derivative expansion method. The conditions on the coefficients of dispersion

and nonlinear terms of this equation have been checked for both stable and

unstable regions in our plasma system. It is found that the negative sign for the

product of the coefficients of dispersion and nonlinear terms is required for the

modulational stability of the waves while positive sign is allowed for a random

perturbation of the amplitude leading to growing and a very huge wave may be

created. Accordingly, the modulational instability, modulational instability

growth rate and rational solution for rogue waves are discussed.

The dependence of physical characteristics of modulational

instability,modulational instability growth rate and rogue waves amplitude on

parameters like the population of nonthermal ions, the carrier wave number,the

equilibrium density of hot dust grains and the charge numbers for negatively

charged hot dust is investigated. On the other hand, under a suitable coordinate

transformation in reductive perturbation theory, a three- dimensional cylindrical

Kadomtsev-Petviashvili (3D-CKP) equation is obtained by reducing the system

of equations. The effect of the nonthermal parameter, the negative charge number

of hot and cold dust on the cylindrical solitary wave properties is investigated.

Furthermore, the solitary wave profiles in both of the radial, axial, and polar

coordinates are examined. The present investigation may be applicable in space

plasma such as F-ring of Saturn.

It is also found that the parameter of the population of nonthermal

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