The Study Of Dust Size Distribution For The Collective Behavior In A Dusty Plasma

Nowadays, with the rapid development of science and technology, the nonlinear science has been the hot topic of investigation because of it's amazing complexity. The study of chaos, fractals and solitons has changed the comprehension of nature for the people. Meanwhile, it has been the pop problem of the nonlinear science.In this paper, the effect of dust size distribution for the dust acoustic solitary wave (DASW) in the cold dusty plasma, the hot dusty plasma, the magnetized dusty plasmas and the dusty plasmas crystals have been studied respectively.In chapter one, the primary content of nonlinear science, the basic definition of plasma physics and the essential theory of perturbation method have been introduced briefly.In chapter two, the small but infinite amplitude dust acoustic wave (DAW) in a collisionless, unmagnetized two-ion-temperature cold dusty plasma has been studied. By using the reductive perturbation method, the Kadomtsev-Petviashvili (KP), Modified KP and Coupled KP equations have been obtained for different cases. It seems that: 1. For the power law distribution (PLD) cases, the DAW in the cold dusty plasma propagate quicker than that of the mono-sized dusty plasma. It is found that the DASW for PLD dusty plasmas is lower than that of the mono-sized dusty plasmas. Moreover, the DASW of PLD dusty plasmas is wider than that of the mono-sized dusty plasmas. For the DASW in PLD dusty plasmas, the amplitude decreases as c increases, but the width and the velocity increases as c increases, where c = a_max/a_min (a_max and a_min refer to the maximum and minimum radii of dust particles respectively). 2. The N-soliton solution of KP equation has been obtained by the Hirota method. Moreover, the interaction process of N-soliton is described by numerical results.In chapter three, the effect of dust size distribution for the two-dimensional DAW in the collisionless, unmagnetized two-ion-temperature hot dusty plasmas has been studied by considering the higher order transverse perturbation. It can be concluded that: For the isothermal and adiabatic cases, the velocity for DAW in the PLD hot dusty plasmas is larger than that of the mono-sized dusty plasmas. Meanwhile, for DASW in the PLD and mono-sized dusty plasmas, the ratio of amplitude increases as σ increases, but the ratio of velocity and the ratio of width decreases as σ increases, where σ = T_d/T_eff (T_d is the temperature of dust particles and T_eff is the effective temperature).In chapter four, the small but infinite amplitude DAW in the magnetized two-ion-temperature dusty plasmas have been investigated. The Zakharov-Kuznetsov (ZK), Modified ZK and Coupled ZK equations have been obtained by using the reductive perturbation method. It indicate that: 1. The polarity of dust particles has important effect on DAW forthe magnetized dusty plasmas: (i) There is a rarefactive DASW when all the dust particles are negatively charged. On the other hand, a compressive DASW exist in this system while the dust particles are positively charged, (ii) For a dusty plasmas with opposite polarity particles, it is noted that the DASW is rarefactive if Otherwise, the DASW is compressive. On the other hand, the stability of the solitary wave solution for the Coupled ZK equation has been discussed by numerical method. It is found that, for the DAW in a magnetized dusty plasmas with dust size distribution, there is a instability to the transverse perturbations with the wave numbers K and L satisfies 0 < (K~2 + L~2)~1/2 < s_c. 2. The N-soliton solution of ZK equation has been obtained by the Hirota method, meanwhile, the different process of two-soliton has been simulated numerically.In chapter five, the characteristic of dust lattice wave (DLW) in a dusty plasma crystal has been studied. It can be concluded that: 1. For the dust lattice solitary wave (DLSW) of weakly inhomogeneous one-dimensional dust lattice, it is found that the amplitude and velocity decreases as time r increases, but the width increases as time r increases: On the other hand, the frequency to, for the envelope wave in dusty plasmas crystal, increases as the wave number k and the charge of dust particles Q increases. 2. It has been investigated that the nonlinear envelope wave in different directions for a two-dimensional hexagonal crystal. It is found that the frequencies in different directions are all increases as the wave number k and the charge of dust particles Q increases. Moreover, the frequency and the velocity in m-direction is larger than that of n-direction.In chapter six, the main results have been summarized and the further works have been introduced.