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Effect of dust size, mass, and charge distributions on the nonlinear dust acoustic solitary waves (DASWs) in a dusty plasma including negatively charged dust particles, electrons, and nonthermal ions has been studied analytically. Dust particles masses and electrical charges are assumed to be proportional with dust size. Using reductive perturbation methods the Kadomtsev-Petviashvili (KP) equation is derived and its
solitary answers are extracted. The coefficients of nonlinear term of KP equation are affected strongly by the size of dust particles when the relative size (the ratio of the largest dust radius to smallest dust radius) is smaller than 2. These coefficients are very sensitive to

The study of dusty plasmas represents one of the most rapidly growing branches of plasma physics. A dusty plasma is an ionized gas containing small particles of solid matter, which acquire a large electric charge by collecting electrons and ions from the plasma. Dust grains or particles are usually highly charged. Charged dust components appear naturally in space environments such as planetary rings, cometary surroundings, interstellar clouds, and lower parts of earth’s ionospheres [

There are many reports on the formation and propagation of DASW in dusty plasma. But far from ideal condition, there are several phenomena which affect the DASW. Presence of nonthermal particles and size distribution are two of them. A nonthermal plasma is in general any plasma which is not in thermodynamic equilibrium, either because the ion temperature is different from the electron temperature, or because the velocity distribution of one of the species does not follow a Maxwell-Boltzmann distribution. The effects of dust temperature and dust charge variation in a dusty plasma with nonthermal ions have been investigated by Duan [

Continuing the former works, we have added the effect of dust size distribution to the model which contains two nonthermal ions at two temperatures, including Maxwellian electrons. In this paper, characteristic features of dust particles with variable size, mass, and electric charge in a nonthermal two-temperature ions dusty plasma are investigated. The mass and charge of dust particles are assumed to be proportional with their size. The paper is organized as follow: following the introduction in Section

We consider the propagation of DASW in collisionless, unmagnetized dusty plasma consisting of highly negatively charged dust grains, electrons, and two-temperature nonthermal ions. The dust particles are much larger and extremely more massive than ions or electrons, but the sizes of dust grains are different. We shall assume that there are

In these equations,

Ions in the plasma are assumed to be nonthermal, so their density can be described by the known Maxwell Boltzmann distribution function. For the dimensionless density number of electrons,

in which

In this part by using the basic equations, the so called KP equation in the plasma with variable dust particle electric charge is derived. KP equation is a fundamental equation, and its solution describes the characteristic of DASW in detail. In order to simplify the equations based on the reductive perturbation theory, it is useful to introduce three independent variables [

in which

By substituting (

Using (

Effects of ions temperature and density on the coefficients of KP equation are very small. In other words, variations of ions temperature and density lead to negligible effects on the coefficients of KP equation in this model.

To plot our data,

For a typical dusty plasma [

The variation of the nonlinear coefficient,

Variation of

Effects of

Variation of

The same effect are occurred for the coefficient

Variation of

Width of generated soliton in this model strongly depends on

Variation of width versus

Profiles of generated solitons in dusty plasma regarding the requirements of our model are presented in Figures

The profile of soliton at different

The profile of soliton at different

In the present paper, nonlinear dust acoustic solitary waves (DASWs) in a cold unmagnetized dusty plasma containing negatively charged dust particles, electrons, and nonthermal ions are investigated. The size of dust particles is taken to be variable, and the charge and mass of dust particles are supposed to be proportional with their size. For this purpose, a reasonable normalization of the hydrodynamic and Poisson’s equations is used to derive the Kadomstev-Petviashvili (KP) equation for our dusty plasma system.

In this model DASWs are found to be rarefactive for all magnitudes of the maximum ratio of dust size

For