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.     

Nonlinear Dust Acoustic Waves in Strongly Coupled Dusty Plasmas with Positively Charged Dust Particles

The nonlinear propagation of dust acoustic waves is investigated in four-component plasmas consisting of positively charged dust grains, trapped ions, nonthermal electrons, and photoelectron due to ultraviolet irradiation.We use generalized viscoelastic hydrodynamic model for strongly coupled dust grain. In the weak nonlinearity limit, a modified Kadomstev–Petviashvili(KP) equation and a modified KP-Burger equation, which have a damping term coming from nonadiabatic charge variation, have been derived in the kinetic regime and hydrodynamic regime, respectively. With the increasing of UV photon flux, the hydrodynamic regime changes to kinetic regime. The approximate analytical line soliton and shock solutions are investigated in the kinetic regime and hydrodynamic regime, respectively.     

Influence of Non-Maxwellian Particles on Dust Acoustic Waves in a Dusty Magnetized Plasma

In this paper an investigation into dust acoustic solitary waves(DASWs) in the presence of superthermal electrons and ions in a magnetized plasma with cold dust grains and trapped electrons is discussed. The dynamic of both electrons and ions is simulated by the generalized Lorentzian(κ) distribution function(DF). The dust grains are cold and their dynamics are studied by hydrodynamic equations. The basic set of fluid equations is reduced to modified Korteweg-de Vries(mKdV) equation using Reductive Perturbation Theory(RPT). Two types of solitary waves, fast and slow dust acoustic soliton(DAS) exist in this plasma. Calculations reveal that compressive solitary structures are possibly propagated in the plasma where dust grains are negatively(or positively) charged. The properties of DASs are also investigated numerically.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion acoustic waves in a dust plasma with ion-dust collision effects is studied. Using the perturbation method, a modified nonlinear Schrodinger equation contains a damping term that comes from the effect of the ion-dust collision is derived. It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion accoustic waves in a dust plasma with ion-dust collision effects is studied.Using the perturbation method,a modified nonlinear Schroedinger equation contains a damping term that comes from the effect of the ion-dust collision is derived.It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Time-Dependent Cylindrical and Spherical Solitary Structures and Double Layers of Dust Ion-Acoustic Waves in Ultra-Relativistic Dense Plasma

Cylindrical and spherical (nonplanar) solitary waves (SWs) and double layers (DLs) in a multi-ion plasma system (containing inertial positively as well as negatively charged ions, non-inertial degenerate electrons, and negatively charged static dust) are studied by employing the standard reductive perturbation method. The modified Gardner (MG) equation describing the nonlinear propagation of the dust ion-acoustic (DIA) waves is derived, and its nonplanar SWs and DLs solutions are numerically analyzed. The parametric regimes for the existence of SWs, which are associated with both positive and negative potential, and DLs which are associated with negative potential, are obtained. The basic features of nonplanar DIA SWs, and DLs, which are found to be different from planar ones, are also identified.     

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 Dynamics of Cylindrical Plasma Waves

The nonlinear dynamics of Langmuir cylindrical waves in a collisionless plasma is studied. The possibility of energy transformation in such waves is considered.     

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)     

Quasi-periodic and Non-periodic Waves in (2+1)-Dimensional Nonlinear Systems

New exact quasi-periodic and non-periodic solutions for the (2 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.     

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.     

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 forunmagnetized dusty plasmas. It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dustcharge are stable even there are some higher order transverse perturbatoins. There are only rarefactive solitary wavesfor this system which has been verified analytically in this paper.     

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.     

Dust Sheared Flow Driven Instability of Dust Drift Waves in a Nonuniform Magnetoplasma

We investigate instability of dust drift waves in a nonuniform dusty magnetoplasma containing transverse sheared plasma flow that is produced by a nonuniform electric field. By using Boltzmann distributed electrons and ions, Poisson’s equation, as well as the dust continuity equation with perpendicular guiding center dust drift speed, we derive an eigenvalue equation, which strongly depends on the profiles of dust sheared flow and dust density gradient. The eigenvalue equation is analytically solved to obtain expressions for the growth rate and threshold of a convective instability arising from resonant interactions between the dust drift waves and sheared flows. The result may be relevant to the understanding of short wavelength (in comparison with the ion gyroradius) electrostatic fluctuations in magnetized plasmas of Saturn rings and in cometary tails. PACS numbers: 52.27.Lw; 52.35.Fp     

Shock Structures in Charge Variable Dusty Plasmas with Effect of Strongly Coupled Dust Particles

A theoretical investigation has been carried out to study the effect of strong electrostatic interaction on the dust acoustic shock structures in strongly coupled dusty plasma with dust charge fluctuations.The fluid approach is employed,in which the strong electrostatic interaction is modeled by effective electrostatic temperature.A Burger-like equation,the coefficients of which are significantly modified by effects of strong coupling and dust charge Ructuation,is derived.It is shown that the combined effects of dust charge Ructuation,the ion/electron temperature,the ion/electron population,and strong coupling effect modify the basic properties of the dust acoustic waves in such a strongly coupled dusty plasma.The results of this work are compared with those observed by some laboratory experiments.     

Some Exact Solutions of Variable Coefficient Cubic-Quintic Nonlinear Schrodinger Equation with an External Potential

By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-quintie nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.     

Description of Finite-amplitude Standing Acoustic Waves Using Convection-diffusion Equations

This paper deals with problems of finite-amplitude standing waves in acoustical resonators of variable cross-section. Set of two one-dimensional partial differential equations in the third approximation, formulated in conservative form, is derived from the fundamental equations of gas dynamics. The model equations which takes into account external driving force, gas dynamic nonlinearities and thermoviscous dissipation are solved numerically in time domain using a central scheme developed for convection-diffusion equations integration. In this paper numerical results for closed air-filled acoustic resonators are presented.     

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     

Nonplanar Electrostatic Solitary Waves in a Relativistic Degenerate Dense Plasma

By employing the reductive perturbation technique, the propagation of cylindrical and spherical ion acoustic solitary waves is studied in an unmagnetized dense relativistic plasma, consisting of relativistically degenerate electrons and cold fluid ions. A modified Korteweg-de-Vries equation is derived and its numerical solutions have been analyzed to identify the basic features of electrostatic solitary structures that may form in such a degenerate Fermi plasma. Different degrees of relativistic electron degeneracy are discussed and compared. It is found that increasing number density leads to decrease the amplitude the width of the ion acoustic solitary wave in both the cylindrical and spherical geometries. The relevance of the work to the compact astrophysical objects, particularly white dwarfs is pointed out.     

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.