非热离子对非均匀碰撞热尘埃等离子体中三维孤波的影响

从理论上研究了非热离子、外部磁场、碰撞对非均匀热尘埃等离子体中三维非线性尘埃声孤波的影响。运用约化摄动法得到描述三维非线性尘埃声孤波的非标准的变系数Korteweg-de Vries(KdV)方程。然后把非标准KdV方程变为标准的变系数KdV方程,并且得到了标准的变系数KdV方程的近似解析解。由此解析解可以看出,非热离子的数目、碰撞、非均匀性、波的斜向传播、尘埃颗粒和非热离子的温度对三维非线性尘埃声孤波的振幅和宽度有很大的影响。外部磁场对三维非线性尘埃声孤波的宽度有影响,而对其振幅没有影响。此外,波的相速度与非热离子、波的斜向传播、尘埃颗粒的温度和非均匀性有关。     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

Dust-acoustic solitary waves in an adiabatic hot dusty plasma

An adiabatic hot dusty plasma (containing non-inertial adiabatic electron and ion fluids, and negatively charged inertial adiabatic dust fluid) is considered. The basic properties of arbitrary amplitude dust-acoustic (DA) solitary waves, which exist in such an adiabatic hot dusty plasma, are explicitly examined by the pseudo-potential approach. To compare the basic properties (critical Mach number, amplitude and width) of the DA solitary waves observed in a dusty plasma containing adiabatic electron, ion and dust fluids with those observed in a dusty plasma containing isothermal electron and ion fluids and adiabatic dust fluid, it has been found that the adiabatic effect of inertia-less electron and ion fluids has significantly modified the basic properties of the DA solitary waves, and that on the basic properties of the DA solitary waves, the adiabatic effect of electron and ion fluids is much more significant than that of the dust fluid.     

Solitons of KdV and modified KdV in dusty plasmas with superthermal ions

For a dusty plasma with a negatively charged dust fluid with Boltzmann distributed electrons and superthermal ions, the dust acoustic solitary waves have been studied in this paper. We derived a Korteweg-de Vries (KdV) equation and a modified KdV equation for different cases. It was shown that the superthermal distributed ion have very important effect on the characters of dust acoustic solitary waves.     

Effect of Weakly Transverse Perturbations on Dust Acoustic Solitary Waves with Adiabatic Variation of Dust Charge

By employing the reductive perturbation technique we derived a Kadomtsev-Petviashvili equation for unmagnetized dusty plasmas,It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dust charge are stable even there are some higher order transverse perturbatoins,There are only rarefactive solitary waves for this system which has been verified analytically in this paper.     

Nonlinear dust-ion-acoustic waves in a multi-ion plasma with trapped electrons

A dusty multi-ion plasma system consisting of non-isothermal (trapped) electrons, Maxwellian (isothermal) light positive ions, warm heavy negative ions and extremely massive charge fluctuating stationary dust have been considered. The dust-ion-acoustic solitary and shock waves associated with negative ion dynamics, Maxwellian (isothermal) positive ions, trapped electrons and charge fluctuating stationary dust have been investigated by employing the reductive perturbation method. The basic features of such dust-ion-acoustic solitary and shock waves have been identified. The implications of our findings in space and laboratory dusty multi-ion plasmas are discussed.     

Cylindrical and spherical dust ion-acoustic solitary waves in quantum plasmas

Dust ion-acoustic solitary waves in unmagnetized quantum plasmas are studied in spherical and cylindrical geometries. Using quantum hydrodynamic model, the electrostatic waves are investigated in the weakly nonlinear limit. A deformed Korteweg-de Vries (dKdV) equation is derived by using the reductive perturbation method and its numerical solutions are also presented. The quantum diffraction and quantum statistical effects incorporated in the system modifies the characteristics of dust ion-acoustic waves in cylindrical and spherical geometries. The role of stationary dust particles in quantum plasmas are also discussed. It is shown that the cylindrical and spherical dust ion-acoustic solitary waves behave quite differently from one-dimensional planar solitary waves in quantum plasmas.     

Dust ion-acoustic solitary waves in a hot adiabatic magnetized dusty plasma

The basic features of obliquely propagating dust ion-acoustic (DIA) solitary waves in a hot adiabatic magnetized dusty plasma (containing adiabatic inertia-less electrons, adiabatic inertial ions, and negatively charged static dust) have been investigated. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation which admits a small amplitude solitary wave solution. The combined effects of plasma particle (electron and ion) adiabaticity, ion-dust collision, and external magnetic field (obliqueness), which are found to significantly modify the basic features of the small but finite-amplitude DIA solitary waves are explicitly examined. The implications of our results in space and laboratory dusty plasmas are briefly discussed.     

Nonplanar dust ion-acoustic solitary and shock waves in a dusty plasma with electrons following a vortex-like distribution

Properties of nonplanar (viz. cylindrical and spherical) dust ion-acoustic (DIA) solitary and shock waves propagating in a dusty plasma containing charge fluctuating stationary dust, inertial warm ions, and non-isothermal electrons following a vortex-like distribution, are investigated by the reductive perturbation method. It has been shown that all the basic features of the DIA solitary and shock waves are significantly modified by the effects of vortex-like electron distribution, dust charge fluctuation, and nonplanar cylindrical and spherical geometries. The implications of our results in some space and laboratory dusty plasma environments are briefly discussed.     

Existing Regions of Either Rarefactive or Compressive Solitary Waves for Particular Dusty Plasma

By deriving a Korteweg-de Vries (KdV) equation for particular dusty plasma, we find the existing regions of solitary waves. The regions of both rarefactive and compressive solitary waves have also been given in this paper for a two-temperature ions and a hot adiabatic dusty fluid, where the dust charges can vary.     

Nonlinear interaction phenomenon of dust acoustic solitary and shock waves in dusty plasma

The effects of head-on collision on dust acoustic (DA) solitary and shock waves in dusty plasma are investigated considering positively charged inertial dust, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and superthermal electrons in the plasma system. The nonlinear Korteweg-de-Vries (KdV) Burger equations are derived taking the extended Poincaré-Lighthill-Kuo method into account to study the characteristic properties of nonlinearity and production of solitary shock due to collisions. The study reveals that the amplitudes and widths of the DA shock waves are decreasing with increasing viscosity, electron to dust density ratio, and dust to ion temperature ratio, while they are increasing due to the presence of superthermal electrons. The nonlinearity of DA waves are enhanced with increasing density ratio of electron to dust and temperature ratio of dust to ion and electron, respectively, but it is reducing with superthermal electrons. The phase shifts of DA solitary waves are found to decrease with rising superthermality of electrons and increase with the density ratio of electron to dust.     

Effect of dust charge variation on dust—acoustic solitary waves in a magnetized two—ion—temperature dusty plasma

The effect of dust charge variation on the dust-acoustic solitary structures is investigated in a warm magnetized two-ion-temperature dusty plasma consisting of a negatively and variably charged extremely massive dust fluid and ions of two different temperatures. It is shown that the dust charge variation as well as the presence of a second component of ions would modify the properties of the dust-acoustic solitary structures and may exite both dust-acoustic solitary holes (soliton waves with a density dip) and positive solitons (soliton waves with a density hump).     

Nonlinear adiabatic models of ion-acoustic waves in dust plasma

Nonlinear adiabatic models of ion-acoustic waves in a dust plasma are developed. The problem of the structure of subsonic periodic and supersonic solitary ion-acoustic waves is exactly solved analytically under the assumption of a constant charge of dust particles; the critical Mach numbers for the solitary wave are determined. The problem of the wave structure is solved numerically for the case when the charge of dust particles was assumed to be variable.     

Dust acoustic wave in a dusty plasmas with streaming ions and nonadiabatic dust charge variation

The effects of nonadiabatic dust charge fluctuation on the nonlinear propagation of the dust acoustic (DA) solitary wave in collisionless dusty plasma with streaming ions have been investigated. By using the reductive perturbation technique, a modified Korteweg-de Vries (mKdV) equation governing the nonlinear waves was derived and the solitary solution of the mKdV equation was also obtained. It was shown that the damping rate of the slow mode DA solitary wave was strongly affected by the ion streaming velocity.     

Effects of axial magnetic field and nonextensivity on small amplitude dust acoustic solitary waves in dusty plasma

The nonlinear propagation of small amplitude dust‐acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann‐distributed electrons and ions with two distinct temperatures following a q‐nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de‐Vries (K‐dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low‐temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Effects of dust size distribution on nonlinear waves in a dusty plasma

For two-dimensional unmagnetized dusty plasmas with many different dust grain species, a Kadomtsev--Petviashvili (KP) equation, a modified KP (mKP) equation and a coupled KP(cKP) equation for small, but finite amplitude dust-acoustic solitary waves are obtained for different physical conditions respectively. The influence of an arbitrary dust size distribution described by a polynomial expressed function on the properties of dust-acoustic solitary waves is investigated numerically. How dust size distribution affects the sign and the magnitude of nonlinear coefficient A(D) of KP (mKP) equation is also discussed in detail. It is noted that whether a compressive or a rarefactive solitary wave exists depends on the dust size distribution in some dusty plasmas.     

Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas

The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg-de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron-ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.     

Propagation features of head-on collision dust acoustic solitary waves in four-component quantum plasmas

ABSTRACT

In framework of the extended Poincaré–Lighthill–Kuo, the properties of dust acoustic (DA) solitary wave’s interaction are investigated in four-component quantum dusty plasma. Two Korteweg–de Vries equations describing the colliding DA solitary waves are derived by eliminating the secularities. By knowing the explicit form of the solitary wave solutions, the leading phase changes, trajectories and phase shifts are obtained, accordingly. The effects of various physical parameters such as the quantum mechanical parameters, the charge ratio between positive and negative dust particles, the mass ratio between negative and positive dust particles and the ratio of electron to ion temperatures are studied extensively. Our findings showed that these parameters play a significant role on the characteristics and basic features of DA solitary waves such as phase shifts in trajectories due to collision. The obtained results may be beneficial to understand well the collision of DA solitary waves that may occur in laboratory plasmas, space plasma as well as in plasma applications.     

Effect of adiabatic variation of dust charges on dust-acoustic solitary waves

The effect of dust charging and the influence of its adiabatic variation on dust-acoustic solitary waves is further studied. A more reasonable normalization for the dust velocity by the dust-acoustic speed is adopted, which varies self-consistently with the system parameters. By employing the reductive perturbation technique we derive small-amplitude dust-acoustic solitons with varying dust charges. The Sagdeev potential shows that only the rarefactive solitary waves exist when the Mach number lies within an appropriate regime depending on the system parameters. An approximate similarity law is obtained and discussed in this dust-charge-fluctuation system.