The Kadomtsev-Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas

Using the reductive perturbation method,we have derived the Kadomtsev-Petviashvili(KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in pair-ion(p-i) plasmas.We have chosen the fluid model for the positive ions,the negative ions,and a fraction of static charged(both positively and negatively) dust particles.Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed.It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma.It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied.It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions,and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions.As the pair-ion plasma mimics the electron-positron plasma,thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.     

Magnetoacoustic solitons in pair-ion fullerene plasma

ABSTRACT

The propagation of magnetoacoustic (fast magnetohydrodynamic) waves in pair-ion (PI) fullerene plasma is studied in the linear and nonlinear regimes. The pair-ion (PI) fullerene plasma is theorized as homogeneous, magnetized, warm and collisionless. Employing multi-fluid magnetohydrodynamic model, the dispersion relation is obtained and wave dispersion effects which appear through ion inertial length are discussed. Using reductive perturbation technique (RPT), the Korteweg–de Vries (KdV) equation is derived and its solution for small but finite amplitude magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is presented. The compressive magnetoacoustic soliton (i.e. positive potential pulse) propagating with super Alfvénic speed is obtained in magnetized PI fullerene plasma. The variations in the amplitude and width of the magnetoacoustic soliton structures are also illustrated by using numerical values of the plasma parameters such as ions' density, temperature difference between fullerene ions and magnetic field intensity, which have been taken from the PI plasma experiments already published in the literature.     

Nonlinear ion-acoustic waves in magnetized plasmas in presence of energetic electrons and positively charged dust

A theoretical investigation has been carried out for exploring different features of ion-acoustic solitary and shock waves in a three-component magnetized plasma containing a mixture of thermal and nonthermal (energetic) inertialess electrons, warm inertial ions, and positively charged stationary dust particles. The standard Korteweg-de Vries (Burgers) equation has been derived by employing the reductive perturbation method, and its solitary (shock) wave solution has been derived and examined analytically as well as numerically. The latter exhibits characteristic properties (amplitude, width, speed, and polarity) of the ion-acoustic solitary and shock waves. It has been shown that the ion-acoustic solitary and shock waves are significantly modified by different plasma parameters (viz. parameter measuring the ratio of dust charge density to ion charge density, parameter measuring the fraction of energetic electrons, parameter measuring ion or electron temperature, and the external magnetic field). The present investigation may help in understanding the physics of various nonlinear phenomena formed in many space plasma systems, (viz. earth's mesosphere, solar wind, and cometary tails) and laboratory devices (laboratory experiments of Samarian et al., Phys. rev. E. 64 , 056407 [2001] and of Fortov et al., New J. Physics 5 , 102 [2003]).     

Roles of positively charged dust in the formation of ion-acoustic subsonic solitary waves in electron-ion-positively charged dust plasmas

The electron-ion-positively charged dust plasma system containing Boltzmann distributed electron species, cold inertial ion species, and stationary positively charged dust (pcd) species are considered. The roles of pcd species in the formation of ion-acoustic (IA) subsonic solitary waves (SWs) are investigated by the pseudo-potential approach, which is valid for arbitrary amplitude time-independent subsonic SWs, as well as by the reductive perturbation method, which is valid for the time-dependent small amplitude subsonic SWs. It is observed that the presence of the pcd species reduces the phase speed of the IA waves, and consequently supports the IA subsonic SWs with the positive wave potential in such electron-ion-pcd plasmas. This is due to the reduction of the space charge electric field by the presence of the pcd species. The applications of the work in space environments (viz. Earth's mesosphere, cometary tails, Jupiter's magnetosphere, etc.), where pcd species have been detected, are briefly discussed.     

Investigation on the resonance phenomena of multi-solitons for the （3＋1）-dimensional Kadomtsev-Petviashvili equation

In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.     

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.     

双麦克斯韦分布尘埃等离子体中尘埃粒子的充电研究

根据充电方程和电荷守恒条件,导出了双麦克斯韦分布的弱电离尘埃等离子体充电频率(电荷弛豫速率),给出了充电电流的计算公式. 对结果分析表明,定向运动速度大小对充电电流和充电频率有一定的影响,充电频率随着定向速度增加而减小,当定向速度远远小于电子的热速度时,充电频率与文献给出的表达式一致. 关键词： 尘埃等离子体 双麦克斯韦分布 充电频率     

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.     

Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects

In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincar\'e--Lighthill--Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail.     

等离子体鞘层中尘埃粒子的分布特性

采用柱槽状电极的流体模型，数值模拟了等离子体鞘层及鞘层中尘埃粒子的分布结构. 研究了尘埃粒子数、粒子大小、电极尺寸等因素对尘埃分布结构的影响. 研究表明：当等离子体密度较高时，鞘层较薄，反之鞘层较厚；当尘埃粒子数少时，尘埃分布形成一层结构，反之则形成多层结构；随电极尺寸的不同，尘埃粒子形成一些复杂而又有趣的结构. 关键词： 尘埃粒子 等离子体鞘层 电极     

Shape-changed propagations and interactions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluids

In this article, we consider the(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP)equation in fluids. We show that a variety of nonlinear localized waves can be produced by the breath wave of the GKP model, such as the(oscillating-) W-and M-shaped waves, rational W-shaped waves, multi-peak solitary waves,(quasi-) Bell-shaped and W-shaped waves and(quasi-) periodic waves. Based on the characteristic line analysis and nonlinear superposition principle, we give the transition conditions analytically. We find the interesting dynamic behavior of the converted nonlinear waves, which is known as the time-varying feature. We further offer explanations for such phenomenon. We then discuss the classification of the converted solutions. We finally investigate the interactions of the converted waves including the semi-elastic collision, perfectly elastic collision, inelastic collision and one-off collision. And the mechanisms of the collisions are analyzed in detail. The results could enrich the dynamic features of the high-dimensional nonlinear waves in fluids.     

两种带电尘埃颗粒的等离子体鞘层玻姆判据

采用流体方程和尘埃充电自洽模型研究了鞘边含有两种尘埃颗粒的等离子体玻姆判据. 通过拟牛顿法数值模拟了鞘边两种尘埃颗粒的存在对尘埃自身充电以及离子马赫数的影响. 两种尘埃颗粒中含量较少的尘埃颗粒数密度的增加, 导致两种尘埃颗粒表面悬浮势一个降低, 一个升高. 含量较少的尘埃颗粒的数密度越多和半径越小, 都会导致离子马赫数增大. 另外鞘边无论何种尘埃颗粒的速度增加, 鞘边离子马赫数都将减小. 关键词： 等离子体鞘层 尘埃颗粒 玻姆判据     

Dust‐acoustic envelope solitons in super‐thermal plasmas

The modulational instability (MI) of the dust‐acoustic waves (DAWs) in an electron‐positron‐ion‐dust plasma (containing super‐thermal electrons, positrons, and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the non‐linear Schrödinger equation (NLSE). To derive the NLSE, the reductive perturbation method was employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super‐thermal electrons, positrons, and ions significantly modifies both the stable and unstable regions. The critical wave number k_c (at which MI sets in) depends on the super‐thermal electron, positron, and ion, and adiabatic dust concentrations.     

双离子成份等离子体的离子声色散关系

以离子温度与电子温度之比为参数,将等离子体介电函数作展开,由此解析地求解了双离子成分等离子体的离子声快、慢波模的色散关系。与现有的其它解析理论相比较,所得到的解析公式更加准确。     

强激光与等离子体相互作用中低频电磁场孤子波的产生及其捕获

用二维粒子模拟程序研究了超短脉冲强激光与等离子体相互作用中局域低频电磁场的产生现象.这种低频电磁场在超短脉冲激光激发尾波场、脉冲后沿产生频率下移的过程中形成.通常它们的振荡频率接近于或低于电子等离子体振荡频率，因而被捕获在等离子体中(即传播速度接近于零).在演化过程中，通常它们以孤子场的形式出现.这种孤子波的形成及其演化与离子运动有极大关系.用相对论强激光脉冲可以产生达到相对论振幅的电磁场孤子波，后者可以把离子加速到非常高的能量.研究还表明，在二维几何位形下，孤子波产生与入射光的偏振态有很大关系.     

Effects of non‐extensive electrons on the sheath of dusty plasmas with variable dust charge

In this study, a detailed investigation of the problem of sheath is presented using the fluid model in a magnetized three‐component dusty plasma system comprising positive ions, dust grains with variable charge and q‐non‐extensive electrons (i.e., the electrons evolve far away from their Maxwellian thermodynamic equilibrium [q = 1]). The effects of q‐non‐extensivity parameter on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath with the presence of the super‐extensive electrons (q < 1) and sub‐extensive electrons (q > 1). In addition, based on the orbital motion limited theory, by taking various forces acting on the dust particle into consideration, the dynamics of the dust located within the sheath, that is, the dust grain charging inside the sheath, is examined under different values of q. It is found that the q‐non‐extensivity has affected significantly the dynamics and the charging process of the dust grains in the sheath.     

Novel loop-like solitons for generalized Vakhnenko equation

A nontraveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation.     

量子尘埃等离子体中尘埃充电对尘埃声波的影响

采用流体动力学方程组和尘埃充电方程组成的自洽模型系统,对量子尘埃等离子体中的尘埃声波波动性质进行了研究。通过线性理论分析方法得到系统的尘埃声波波动方程及其色散关系,并对色散关系进行了数值分析。研究表明：充电效应定性地修正了尘埃声波的色散特性,引起尘埃声波的耗散,其耗散强度主要与尘埃等离子体的参数有关。最后,分析了引起尘埃声波耗散的物理原因。     

Nonautonomous solitons in the continuous wave background of the variable-coefficient higher-order nonlinear Schro¨dinger equation

We reduce the variable-coefficient higher-order nonlinear Schrdinger equation (VCHNLSE) into the constantcoefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.     

Effect of Bohm quantum potential in the propagation of ion–acoustic waves in degenerate plasmas

A theoretical investigation has been carried out on the propagation of the ion–acoustic(IA) waves in a relativistic degenerate plasma containing relativistic degenerate electron and positron fluids in the presence of inertial non-relativistic light ion fluid. The Korteweg-de Vries(K-dV), modified K-dV(m K-dV), and mixed m K-dV(mm K-dV) equations are derived by adopting the reductive perturbation method. In order to analyze the basic features(phase speed, amplitude, width,etc.) of the IA solitary waves(SWs), the SWs solutions of the K-dV, m K-dV, and mm K-d V are numerically analyzed. It is found that the degenerate pressure, inclusion of the new phenomena like the Fermi temperatures and quantum mechanical effects(arising due to the quantum diffraction) of both electrons and positrons, number densities, etc., of the plasma species remarkably change the basic characteristics of the IA SWs which are found to be formed either with positive or negative potential. The implication of our results in explaining different nonlinear phenomena in astrophysical compact objects, e.g.,white dwarfs, neutron stars, etc., and laboratory plasmas like intense laser–solid matter interaction experiments, etc., are mentioned.