尘埃等离子体中非线性波的叠加效应及稳定性问题

研究了小的有限振幅的无磁场尘埃等离子体中的非线性波.在一维情况下由Korteweg de Veries (KdV)方程来描述,考虑了二维情况下尘埃等离子体中尘埃颗粒上电荷的变化效应以及双温度离子效应后,尘埃等离子体受到横向高阶扰动后动力学方程由Kadomtsev-Petviashvili(KP)方程来描述.在此基础上,研究了以任意夹角传播的两个及三个孤立子的相互作用问题,考虑非线性效应后振幅相等的双孤立子在相互作用区域内振幅最大值是单个孤立子振幅的4倍,振幅相等的三孤立子在相互作用区域内振幅最大值是单个孤立子振幅的9倍.研究还表明波的传播方向受到横向高阶扰动后是稳定的.     

等离子体中非线性朗谬尔波的哈密顿描述

研究了在双离子（H^ ,O^ )成份等离子体中的非线性朗谬尔波的特性,从流体方程出发,考虑低频离子运动的完全非线性和双极势的色散,得到了描述高频电场缓变振幅与低频势扰动的耦合方程组。利用哈密顿方法,在小振幅情况下,对方程组解耦合,利用Sagdeev势方法,对孤立波的性状进行了讨论,结果表明,双离子成份等离子体中双极势的孤立子的幅度相对电子,离子等离子体的双极势孤立子的幅度要大,而相应的高频电场强度的幅度相对要小,相应的孤立子的速度传播区也较小。     

强耦合尘埃等离子体中正电扰动下的尘埃声激波

研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

尘埃等离子体中朗缪尔波的非线性调制

研究了尘埃等离子体中尘埃声波（ＤＡＷ）和尘埃离子声波（ＤＩＡＷ）对朗缪尔波的非线性调制。在小而有限振幅极限下,得到了朗缪尔波的包络孤立子。对于朗缪尔波与尘埃声波的非线性耦合,包络孤立子存在两个速度传播区;而对于与尘埃离子声波的耦合,只有一个传播区     

低β尘埃等离子体中尘埃-动力学阿尔文孤立波

用三成分的流体模型,研究了尘埃等离子体中的尘埃－动力阿尔文波。导出了描述离子密度变化的非线性的能量积分方程。在小振幅极限下,得到密度的孤立子解,对Ｓａｇｄｅｅｖ势进行了数值研究。结果表明,在不同的参数区域,可以激发具有密度坑或密度隆起的孤立波;随着尘埃密度的增加,密度坑变浅,密度隆起增大。     

绝热电荷扰动对非均匀热尘埃等离子体中三维孤波的影响

尘埃颗粒上不断有电子流和离子流的出入以及二次电离、光电离等因素,所以尘埃颗粒上的带电量不是一个常量而是随着时间和空间变化的,因此尘埃电荷成为尘埃等离子体中的一个新的动力学变量,研究其对等离子体中各类非线性过程的作用成为尘埃等离子体物理中的一个重要课题.当今对于非均匀尘埃等离子中非线性波的研究大多数都集中于一维,对于三维非线性波的研究非常少.基于这种情况,在考虑非均匀性、尘埃颗粒绝热电荷扰动以及外部磁场等物理因素的情况下,运用约化摄动方法得出描述三维孤波的变系数的Korteweg-de Vries(KdV)方程.由结果可以看出,非均匀性、电荷扰动、外部磁场、斜向传播、尘埃温度对三维非线性波的传播有着极大的影响.利用适当的变换,得到了变系数方程的近似解.     

热尘埃等离子体中(2+1)维尘埃声孤波的传播特征

研究了由尘埃颗粒、电子和非热离子所组成的非磁化热尘埃等离子体中(2+1)维非线性尘埃声孤波的传播特征.首先,利用约化摄动法推导得到了用来描述(2+1)维非线性尘埃声孤波的Kadomtsev-Petviashvili(KP)方程,并采用行波解法进行了定性分析,从而获得了该系统的相图及Sagdeev势方程;然后,利用数学软件的数值模拟分析方法讨论了等温和绝热两种状态下,热尘埃等离子体系统中不同参数对KP方程的非线性系数、色散系数、系统相图、Sagdeev势函数及孤立波解的影响.最终,研究结果表明:等温和绝热状态下,尘埃颗粒的质量、电子和非热离子的温度、数密度及分布状态等多种系统参数对非线性尘埃声孤波的振幅、宽度及波形等传播特征均存在重要影响.     

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。     

五阶克尔非线性光纤放大器中光脉冲的传输特性

以变系数高阶非线性薛定谔方程为理论模型,对光脉冲在具有五阶非线性克尔效应光纤放大器中的传输特性进行了研究.在加入振幅微扰、相位扰动、噪声微扰的情况下,数值模拟了亮孤波、灰孤波和黑孤波在光纤系统中的传输稳定性,并且讨论了孤子间的相互作用.数值模拟结果表明:在有限的微扰下,三种光脉冲具有良好的传输稳定性.     

Effect of Second Nonthermal Ion on the Characteristics of Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Variable Dust Charge

The nonlinear dust acoustic solitary waves in a magnetized dusty plasma with nonthermal ions and variable dust electric charge is studied analytically. Using reductive perturbation method the Zakharov‐Kuznetsov (ZK) equation is derived and effect of nonthermal coefficient, external magnetic field, and variable dust electric charge on the amplitude and width of soliton in dusty plasma is investigated. With increasing the rate of dust charge variation with respect of plasma potential, the amplitude of generated solitary waves in magnetized dusty plasma increases to a constant magnitude while its width decreases. Increasing the nonthermal ions coefficient leads to a noticeable decrease in the amplitude of solitons while the width of soliton increases. The amplitude of generated solitary waves in such a dusty plasma is independent of applied external magnetic field but we will have more localized solitons with increasing the external magnetic field strength. It is found that solitons are strongly influenced by the direction of external magnetic field. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of nonthermal ion distribution and dust temperature on nonlinear dust acoustic solitary waves

The effects of nonthermal ion distribution and finite dust temperature are incorporated in the investigation of nonlinear dust acoustic waves in an unmagnetized dusty plasma. Sagdeev pseudopotential method which takes into account the full nonlinearity of plasma equations, is used here to study solitary wave solutions. Possibility of co-existence of refractive and compressive solitons as a function of Mach number, dust temperature and concentration of nonthermal ions, is considered. For the fixed value of nonthermal ions, it is found that the effect of increase in dust temperature is to reduce the range of co-existence of compressive and refractive solitons. Particular concentration of nonthermal ions results in disappearance of refractive solitons while the decrease in dust temperature, at this concentration restores the lost refractive solitons.     

Large-amplitude dust acoustic solitons in an opposite polarity dusty plasma with generalized polarization force

Linear and nonlinear dust acoustic(DA)waves have been investigated in an opposite polarity dusty plasma comprising negatively and positively charged dust grains,Maxwellian electrons and ions,including the generalized polarization force effect.The properties of linear DA waves have been significantly altered by the dual dust polarity and polarization force.Large amplitude DA solitons have been discussed in the framework of the Sagdeev potential technique.Our results show that both rarefactive and compressive solitons can exist in such a dusty plasma.The basic features of the Sagdeev potential have been examined under the effect of the polarization force parameter R,the ratio of the charge number of the positive dust to that of the negative dust Z,and the Mach number M.The results show that these parameters play a significant role in determining the region of existence of large amplitude DA solitons.     

Nonlinear Dust Acoustic Waves in Dissipative Space Dusty Plasmas with Superthermal Electrons and Nonextensive Ions

The nonlinear characteristics of the dust acoustic(DA)waves are studied in a homogeneous,collisionless,unmagnetized,and dissipative dusty plasma composed of negatively charged dusty grains,superthermal electrons,and nonextensive ions.Sagdeev pseudopotential technique has been employed to study the large amplitude DA waves.It(Sagdeev pseudopotential)has an evidence for the existence of compressive and rarefractive solitons.The global features of the phase portrait are investigated to understand the possible types of solutions of the Sagdeev form.On the other hand,the reductive perturbation technique has been used to study small amplitude DA waves and yields the Korteweg-de Vries-Burgers(Kd V-Burgers)equation that exhibits both soliton and shock waves.The behavior of the obtained results of both large and small amplitude is investigated graphically in terms of the plasma parameters like dust kinematic viscosity,superthermal and nonextensive parameters.     

Nonlinear localized dust acoustic waves in a charge varying dusty plasma with trapped ions

The problem of nonlinear variable charge dust acoustic waves in a dusty plasma with trapped ions is revisited. The correct non-isothermal ion charging current is presented for the first time based on the orbit motion limited (OML) approach. The variable dust charge is then expressed in terms of the Lambert function and we take advantage of this new transcendental function to investigate nonlinear localized dust acoustic waves in a charge varying dusty plasma with trapped ions more rigorously.     

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.     

Electrostatic dust-acoustic envelope solitons in an electron-depleted plasma

A standard nonlinear Schrödinger equation has been established by using the reductive perturbation method to investigate the propagation of electrostatic dust-acoustic waves, and their modulational instability as well as the formation of localized electrostatic envelope solitons in an electron-depleted unmagnetized dusty plasma system comprising opposite polarity dust grains and super-thermal positive ions. The relevant physical plasma parameters (viz., charge, mass, number density of positive and negative dust grains, and super-thermality of the positive ions, etc.) have rigorous impact to recognize the stability conditions of dust-acoustic waves. The present study is useful for understanding the mechanism of the formation of dust-acoustic envelope solitons associated with dust-acoustic waves in the laboratory and space environments.     

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.