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 Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

Cylindrical and spherical electron-acoustic Gardner solitons and double layers in a two-electron-temperature plasma with nonthermal ions

Cylindrical and spherical Gardner solitons (GSs) and double layers (DLs) in a two-electron-temperature plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the electron-acoustic (EA) waves is derived, and its nonplanar GS and DL solutions are numerically analyzed. The parametric regimes for the existence of GSs, which are associated with both positive and negative potential, and DLs which are associated with positive potential, are obtained. The basic features of nonplanar EA GSs, and DLs, which are found to be different from planar ones, are also identified. The implications of our results in space and laboratory plasmas are briefly discussed.     

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.     

Effect of superthermal electrons on dust-acoustic Gardner solitons in nonplanar geometry

The properties of nonplanar (cylindrical and spherical) dust-acoustic solitary waves (DASWs) in an unmagnetized, collisionless three-component dusty plasma, whose constituents are negatively charged cold dust fluid, superthermal/non-Maxwellian electrons (represented by kappa distribution) and Boltzmann distributed ions, are investigated by deriving the modified Gardner (MG) equation. The well-known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar DA Gardner solitons (GSs) are discussed. It is seen that the properties of nonplanar DAGSs (positive and negative) significantly differ as the value of spectral index κ changes.     

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.     

Streaming instability of dust-acoustic mode with helical wavefronts

Making use of the kinetic approach for plasma species, the electrostatic twisted dust-acoustic (DA) waves are studied in a collisionless unmagnetized multi-component dusty plasma consisting of electrons, singly ionized positive ions and charged massive dust grains. The Vlasov-Poisson equations are coupled together to obtain a generalized response function by using the Laguerre-Gaussian (LG) perturbed electrostatic potential and distribution function in the paraxial limit. The dispersive properties and growth rate instability of twisted DA waves are examined with distinct OAM states in a multi-component dusty plasma. Various significant modifications associated with the real wave frequency and growth rate are shown with respect to twist parameter and dust concentration. It is examined that dust concentration enhances the growth rate of twisted DA waves, whereas an increase in twist parameter reduces the growth rate instability. The excitation of twisted DA mode is also found to enhance with streaming speed of inertialess electrons. Our results may be useful for particle transport and trapping phenomena due to wave excitation in laboratory dusty plasmas.     

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.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains, kappa-distributed ions as well as electrons. The nonplanar DA solitons are studied based on the reductive perturbation technique. It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied. It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

Spherical Kadomtsev-Petviashvili Solitons in a Suprathermal Complex Plasma

The nonlinear aspects of nonplanar dust acoustic (DA) solitary waves are investigated in an unmagnetized complex plasma comprising of cold dust grains,kappa-distributed ions as well as electrons.The nonplanar DA solitons are studied based on the reductive perturbation technique.It is shown that the evolution of DA solitons is governed by a spherical Kadomtsev-Petviashvili (sKP) equation and then the impact of suprathermality on the spatial structure as well as the nature of DA soliton is studied.It seems that the properties of DA solitons in nonplanar geometry are quite different from that of the planar solitons.     

On the dielectric response function and dispersion relation in strongly coupled magnetized dusty plasmas

Using the generalized viscoelastic fluid model, we derive the dielectric response function in a strongly coupled dusty magnetoplasma which reveals two different dust acoustic(DA) wave modes in the hydrodynamic and kinetic limits. The effects of the strong interaction of dust grains and the external magnetic on these DA modes, as well as on the shear wave are examined. It is found that both the real and imaginary parts of DA waves are significantly modified in strongly coupled dusty magnetoplasmas. The implications of our results to space and laboratory dusty plasmas are briefly discussed.     

On the numerical solution of nonplanar dust-acoustic super rogue waves in a strongly coupled dusty plasma

The occurrence of cylindrical and spherical low-frequency dust-acoustic freak waves (DAFWs) in a strongly coupled dusty plasma is numerically investigated in the framework of the phenomenological generalized hydrodynamic model. The basic equations are reduced to a modified/nonplanar nonlinear Schrödinger equation (mNLSE) using a reductive perturbation method. The existing regions of instability structures have been carefully identified. For studying the propagation of rogue waves in case of nonplanar (cylindrical and spherical coordinates), the mNLSE has been solved numerically. The effects of nonplanar geometries on the basic features of the DAFWs for the first- and second-orders rogue waves are discussed. Finally, our results are of relevance in ultradense situations where nonplaner geometrical effects are significant. In particular, we expect for our findings to be important to understand the DA breathers experimentally in a strongly coupled dusty plasma.     

Large Amplitude Dust Ion Acoustic Solitons and Double Layers in Dusty Plasmas with Ion Streaming and High-Energy Tail Electron Distribution

Large amplitude dust ion acoustic （DIA） solitons as well as double layers （DLs） are studied in a dusty plasma having a high-energy-tail electron distribution. The influence of electron deviation from the Maxwellian distribution and ion streaming on the existence domain of solitons is discussed in the （M, f） space using the pseudo-potential approach. It is found that in the presence of streaming ions and for a fixed f, solitons may appear for larger values of M. This means that in the presence of ion streaming, high values of the Mach number are needed to have soliton. The DIA solitary waves profile is highly sensitive to the ion streaming speed. Their amplitude is found to decrease with an increase of the ion streaming speed. In addition, we find that the ion streaming effect may lead to the appearance of double layers. The results of this axticle should be useful in understanding the basic nonlinear features of DIA waves propagating in space dusty plasmas, especially those including a relative motion between species, such as comet tails and solar wind streams, etc.     

Bifurcation analysis of nonlinear and supernonlinear dust–acoustic waves in a dusty plasma using the generalized (r,q) distribution function for ions and electrons

Bifurcation analysis of dust acoustic (DA) periodic waves in three components, unmagnetized dusty plasma system is investigated using the generalized (r, q) distribution function for ions and electrons. Depending on the different parameters of the system considered, all possible phase portraits, including periodic, homoclinic, superperiodic, and superhomoclinic trajectories, are presented. The existence of rarefactive and compressive solitary waves is proved. Also, the plasma system under consideration supports both nonlinear and supernonlinear DA periodic waves. It has been found that the double spectral indices r and q play a decisive effect on the bifurcation of the waves.     

Large amplitude ion-acoustic double layers in a plasma havingvariable-charge dust grain particles

The dust grain charging effect on large amplitude ion-acoustic double layers in a dusty plasma are investigated by the numerical calculation. The nonlinear structures of ion-acoustic double layers are examined, showing that the characteristics of the double layer sensitively depend on the dust charging effect, the influence of the ion temperature, the electrostatic potential, and the Mach number. The flow of the plasma current to the surface of dust particles increases the dust charge numbers. The effect of the ion temperature decreases the propagation speed of the ion-acoustic double layers and decreases the dust charge numbers. It is found that rarefactive double layers can propagate in this system. New findings of large amplitude ion-acoustic double layers with the dust charging effect and finite ion temperature in a dusty plasma are predicted     

Small amplitude dust-acoustic soliton energy in dusty plasmas with suprathermal polarization force

The effect of suprathermal polarization force on both linear and weakly nonlinear dust-acoustic solitary structures in a three-component dusty plasma is investigated. For this purpose, a new expression of the polarization force acting on dust particles that include the electronic suprathermal effect is derived. The results are applied to two different experimental dusty plasmas. We have found that the polarization force acting on the dust grains decreases as the electron suprathermality becomes more significant. In addition, we have shown that, for a given value of the spectral index κ , the polarization force magnitude fluctuates from one plasma to another. The changes arising in the propagation of small-amplitude dust-acoustic (DA) solitons due to the presence of this suprathermal polarization force are also analysed. Interestingly, an increase in the magnitude of the polarization force leads to an increase in the amplitude and width of DA soliton and provides more energy to the motion of this soliton.     

Arbitrary amplitude solitary waves and double layers in an ultra-relativistic degenerate dense dusty plasma

Arbitrary amplitude solitary waves (SWs) and double layers (DLs) in an ultra-relativistic degenerate dense dusty plasma (containing ultra-relativistic degenerate ultra-cold electron fluid, inertial ultra-cold ion fluid, and negatively charged static dust) have been investigated by the pseudo-potential approach. It has been found that for δ=1 (where δ is the ratio of nonlinear wave speed to linear wave phase speed) extremely large amplitude DLs with negative potential exist for μ=0.537 (where μ is the ratio of dust charge density to ion charge density) and SWs with negative potential exist for 1>μ>0.537. It is also shown that for δ>1 only SWs with positive potential exist for 0?μ<0.537, but SWs with positive potential coexist with SWs or DLs with a negative potential for 0.537>μ>0.851. The implications of our results in some compact astrophysical objects, particularly, in white dwarfs and neutron stars, have been briefly discussed.     

Formation of dust-acoustic shock waves in a strongly coupled cryogenic dusty plasma

The nonlinear propagation of ultra-low-frequency dust-acoustic (DA) waves in a strongly coupled cryogenic dusty plasma has been investigated, by using the Boltzmann distributed electrons and ions, as well as modified hydrodynamic equations for strongly coupled charged dust grains. The reductive perturbation technique is used to derive the Burger equation. It is shown that strong correlations among negatively charged dust particles acts like a dissipation, which is responsible for the formation of the DA shock waves. The latter are associated with the negative potential, i.e. with the compression of negatively charged cryogenic dust particle density. It is also found that the effective dust-temperature, which arises from electrostatic interactions among negatively charged dust particles, significantly affects the height of the DA shock structures. New laboratory experiments at cryogenic temperature should be conducted to verify our theoretical prediction.     

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.     

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.