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.     

Small-amplitude nonlinear dust acoustic wave a magnetized dustyplasma with charge fluctuation

Some properties of nonlinear dust acoustic waves in magnetized dusty plasma with variable charges by reductive perturbation technique have been studied. The effect of adiabatic dust charge variations under the assumption that the ratio of dust charging time to the dust hydrodynamical time is very small, and the nonadiabatic dust charges variations under the assumption that the same ratio is small but finite, are also incorporated. It is seen that the magnetic field and the dust charge variations significantly modify the wave amplitude. It is also seen that in case of adiabatic charge variations, the Korteweg-de Vries (KdV) equation governs the nonlinear dust acoustic wave, whereas in case of nonadiabatic dust charge variations, the wave is governed by the KdV Burger equation. Nonadiabaticity generated anomalous dissipative effect causes generation of the dust acoustic shock wave. Numerical integration of KdV Burger equation shows that the dust acoustic wave admits oscillatory (dispersion dominant) or monotone (dissipation dominant) shock solutions depending on the magnitude of the coefficient of the Burger term     

Travelling Wave Solution of Korteweg-de Vries-Burger's Equation

An attempt has been made to obtain exact analytical travelling wave solution of Korteweg-de Vries-Burger's (KdVB) equation by the so-called tanh-method. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method. It is found that an exact solution of the KdVB equation is obtained by tanh-method, provided the parameters involved satisfy a constraint relation. However a special exact analytical solution can be obtained where no such restriction is necessary. This solution has the structure of a shock wave. Numerical solution is also obtained for travelling wave with or without the assumption of the constraint relation. We have also found a singular solution in terms of cosech and coth functions.     

Dust acoustic shock wave generation due to dust charge variation in a dusty plasma

In a dusty plasma, the non-adiabaticity of the charge variation on a dust grain surface results in an anomalous dissipation. Analytical investigation shows that this results in a small but finite amplitude dust acoustic (DA) wave propagation which is described by the Korteweg-de Vries-Burger equation. Results of the numerical investigation of the propagation of large-amplitude dust acoustic stationary shock wave are presented here using the complete set of non-linear dust fluid equations coupled with the dust charging equation and Poisson equation. The DA waves are of compressional type showing considerable increase of dust density, which is of significant importance in astrophysical context as it leads to enhanced gravitational attraction considered as a viable process for star formation. The DA shock transition to its far downstream amplitude is oscillatory in nature due to dust charge fluctuations, the oscillation amplitude and shock width depending on the ratioω _pd/V_ch and other plasma parameters Article presented at the International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.     

Nonplanar Electron - Acoustic Shock Waves with Superthermal Hot Electrons

Nonplanar electron-acoustic shock waves having superthermal hot electrons are investigated with two temperature electrons model in unmagnetized plasma. Using reductive perturbation method, Korteweg-de Vries-Burgers (KdVB) equation is obtained in the cylindrical/spherical coordinates. Dissipation effect is introduced in the model by means of kinematic viscosity term. On the basis of the solutions of KdVB equation, variation of shock waves features (amplitude, velocity and width) with different plasma parameters are analysed. KdV-Burgers equation always leads to monotonic solitons and no oscillatory peak may appear. The combined effect of particle density (α), superthermal parameter (κ), electron temperature ratio (??) and kinetic viscosity (η₀) is numerically studied, and it is observed that these parameters significantly change the properties of the shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyse the soliton features in laboratory as well as in the space environments.     

Longitudinal Dust Lattice Shock Wave in a Strongly Coupled Complex Dusty Plasma

The effect of hydrodynamical damping that arises due to the irreversible processes within the system have been studied on 1D nonlinear longitudinal dust lattice wave (LDLW) in homogeneous strongly coupled complex (dusty) plasma. Analytical investigation shows that the nonlinear wave is governed by Korteweg‐de Vries Burgers' equation. This hydrodynamical damping induced dissipative effect is responsible for the Burgers' term that causes the generation of shock wave in dusty plasma crystal. Numerical investigation on the basis of the glow‐discharge plasma parameters reveal that LDLW exhibits both oscillatory and monotonic shock. The shock is compressive in nature and its strength decreases (increases) with the increase of the shielding parameter κ (characteristic length L). The effects of dust‐neutral collision are also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Specifications of dust-ion-acoustic shock waves affected by dust charge variation in four-component dissipative quantum plasma

ABSTRACT

Nonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (H_c) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices.     

Shock waves in a rotating non-Maxwellian viscous dusty plasma

A theoretical model is presented to study the characteristics of dust acoustic shock in a viscous, magnetized, rotating dusty plasma at both fast and slow time scales. By employing the reductive perturbation technique, the non-linear Zakharov–Kuznetsov–Burger (ZKB) equation is derived for both cases when the dust is inactive and dynamic (fast and slow time scales). Both electrons and ions are considered to follow the kappa/Cairns distribution. It is observed that in both cases, i.e. when dust is in the background and active, viscosity plays a key role in dissipation for the propagation of acoustic shock. Magnetic field and rotation are responsible for the dispersive term. Superthermality is found to affect significantly the formation of the shock wave along with viscous nature of plasma, whereas the dust charge affects the non-linear coefficient of the ZKB equation. The present investigation may be beneficial to the understanding of the rotating plasma, in particular the experiments being carried out.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Nonlinear Dispersive and Dissipative Electrostatic Structures in Two-Dimensional Electron-Positron-Ion Quantum Plasma

The nonlinear features of two-dimensional ion acoustic(IA) solitary and shock structures in a dissipative electron-positron-ion(EPI) quantum plasma are investigated. The dissipation in the system is taken into account by incorporating the kinematic viscosity of ions in plasmas. A quantum hydrodynamic(QHD) model is used to describe the quantum plasma system. The propagation of small but finite amplitude solitons and shocks is governed by the Kadomtsev-Petviashvili-Burger(KPB) equation. It is observed that depending on the values of plasma parameters(viz.quantum diffraction, positron concentration, viscosity), both compressive and rarefactive solitons and shocks are found to exist. Furthermore, the energy of the soliton is computed and possible solutions of the KPB equation are presented numerically in terms of the monotonic and oscillatory shock profiles     

Nonlinear Waves in Nonuniform Complex Astrocloud

The global nonlinear gravito‐electrostatic eigen‐fluctuation behaviors in large‐scale non‐uniform complex astroclouds in quasi‐neutral hydrodynamic equilibrium are methodologically analyzed. Its composition includes warm lighter electrons, ions; and massive bi‐polar multi‐dust grains (inertial) with partial ionization sourced, via plasma‐contact electrification, in the cloud plasma background. The multi‐fluidic viscous drag effects are conjointly encompassed. The naturalistic equilibrium inhomogeneities, gradient forces and nonlinear convective dynamics are considered without any recourse to the Jeans swindle against the traditional perspective. An inho‐mogeneous multiscale analytical method is meticulously applied to derive a new conjugated non‐integrable coupled (via zeroth‐order factors) pair of variable‐coefficient inhomogeneous Korteweg de‐Vries Burger (i ‐KdVB) equations containing unique form of non‐uniform linear self‐consistent gradient‐driven sinks. A numerical illustrative scheme is procedurally constructed to examine the canonical fluctuations. It is seen that the eigenspectrum coevolves as electrostatic rarefactive damped oscillatory shock‐like structures and self‐gravitational compressive damped oscillatory shock‐like patterns . The irregular damping nature is attributable to the i ‐KdVB sinks. The aperiodicity in the hybrid rapid small downstream wavetrains is speculated to be deep‐rooted in the quasi‐linear gravito‐electrostatic interplay. The phase‐evolutionary dynamics grow as atypical non‐chaotic fixed‐point attractors . We, finally, indicate tentative astronomical applications relevant in large‐scale cosmic structure formation aboard facts and faults. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Planar and non-planar ion acoustic shock waves in electron-positron-ion plasmas

Ion acoustic shock waves (IASW's) are studied in an unmagnetized plasma consisting of electrons, positrons and adiabatically hot positive ions. This is done by deriving the Kortweg-deVries-Burger (KdVB) equation under the small amplitude perturbation expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. It is found that the strength of ion acoustic shock wave is maximum for spherical, intermediate for cylindrical, and minimum for planar geometry. It is observed that the positron concentration, ratio of ion to electron temperature, and the plasma kinematic viscosity significantly modifies the shock structure. Finally, it is found that the temporal evolution of the non-planar IASW's is quite different by comparison with the planar geometry. The relevance of the present study with regard to the dense astrophysical environments is also pointed out.     

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.     

Novel solitary and shock wave solutions for the generalized variable-coefficients (2+1)-dimensional KP-Burger equation arising in dusty plasma

The 2-D generalized variable-coefficient Kadomtsev-Petviashvili-Burgers equation representing many types of acoustic waves in cosmic and/or laboratory dusty plasmas is reduced by the modified classical direct similarity reduction method to nonlinear ordinary differential equation of fourth-order. Using the extended Riccati equation mapping method for solving the reduced equation, many new shock wave, solitary wave and periodic wave solutions are obtained with some constraints between the variable coefficients. Finally, some physical interpretations for the obtained solutions as, bright and dark solitons, periodic solitary wave, and shock wave in dust plasma and quantum plasma are achieved.     

Time fractional effect on ion acoustic shock waves in ion-pair plasma

The nonlinear properties of ion acoustic shock waves are studied. The Burgers equation is derived and converted into the time fractional Burgers equation by Agrawal’s method. Using the Adomian decomposition method, shock wave solutions of the time fractional Burgers equation are constructed. The effect of the time fractional parameter on the shock wave properties in ion-pair plasma is investigated. The results obtained may be important in investigating the broadband electrostatic shock noise in D- and F-regions of Earth’s ionosphere.     

非线性LC电路方程的显式精确行波解

理论上考察了具有耗散的非线性LC电路中的行波. 借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程. 一致地获得了丰富的显式精确解析行波解, 包括精确冲击波解和奇异的行波解, 和三角函数有理形式的周期波解. 关键词： LC电路')" href="#">非线性LC电路 非线性耗散波动方程 冲击波 周期波     

Effects of polarization force and nonthermal ions on dust-acoustic (DA) shock waves in a strongly coupled dusty plasma with positively charged dust

The nonlinear propagation of the dust-acoustic (DA) waves in a strongly coupled dusty plasma containing Maxwellian electrons, nonthermal ions, and positively charged dust is theoritically investigated by a Burgers equation. The effects of the polarization force (which arises due to the interaction between electrons and highly positively charged dust grains) and nonthermal ions are studied. DA shock waves are found to exist with positive potential only. It represents that the strong correlation among the charged dust grains is a source of dissipation, and is responsible for the formation of DA shock waves. The effects of polarization force and nonthermal ions significantly modified the basic features of DA shock waves in strongly coupled dusty plasma.     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Effects of dust size distribution in ultracold quantum dusty plasmas

The effect of dust size distribution in ultracold quantum dusty plasmas are investigated in this paper. How the dispersion relation and the propagation velocity for the quantum dusty plasma vary with the system parameters and the different dust distribution are studied. It is found that as the Fermi temperature of the dust grains increases the frequency of the wave increases for large wave number dust acoustic wave. The quantum parameter of H_d also increases the frequency of the large wave number dust acoustic wave. It is also found that the frequency ω₀ and the propagation velocity v₀ of quantum dust acoustic waves all increase as the total number density increases. They are greater for unusual dusty plasmas than those of the usual dusty plasma.