Dust ion acoustic travelling waves in the framework of a modified Kadomtsev-Petviashvili equation in a magnetized dusty plasma with superthermal electrons

For the critical values of the parameters q and V, the work (Samanta et al. in Phys. Plasma 20:022111, 2013b) is unable to describe the nonlinear wave features in magnetized dusty plasma with superthermal electrons. To describe the nonlinear wave features for critical values of the parameters q and V, we extend the work (Samanta et al. in Phys. Plasma 20:022111, 2013b). To extend the work, we derive the modified Kadomtsev-Petviashvili (MKP) equation for dust ion acoustic waves in a magnetized dusty plasma with q-nonextensive velocity distributed electrons by considering higher order coefficients of ?. By applying the bifurcation theory of planar dynamical systems to this MKP equation, the existence of solitary wave solutions of both types rarefactive and compressive, periodic travelling wave solutions and kink and anti-kink wave solutions is proved. Three exact solutions of these above waves are determined. The present study could be helpful for understanding the nonlinear travelling waves propagating in mercury, solar wind, Saturn and in magnetosphere of the Earth.     

Head on collision of dust ion acoustic solitary waves in magnetized quantum dusty plasmas

The Head on collision of dust ion acoustic solitary waves (DIASWs) in a magnetized quantum dusty plasma is investigated. Two sides Korteweg-de Vries (KdV) equations are obtained, the analytical phase shifts and the trajectories after the head-on collision of two DIASWs in a three species quantum dusty plasma are derive by using the extended version of Poincaré-Lighthill-Kuo (PLK) method. It is observed that the phase shifts are significantly affected by the quantum parameters like quantum diffraction, the ion cyclotron frequency and the ratio of the densities of electrons to ions.     

Bifurcations of electron acoustic traveling waves in an unmagnetized quantum plasma with cold and hot electrons

Bifurcations of nonlinear electron acoustic solitary waves and periodic waves in an unmagnetized quantum plasma with cold and hot electrons and ions has been investigated. The one dimensional quantum hydrodynamic model is used to study electron acoustic waves (EAWs) in quantum plasma. Applying the well known reductive perturbation technique (RPT), we have derived a Korteweg-de Vries (KdV) equation for EAWs in an unmagnetized quantum plasma. By using the bifurcation theory and methods of planar dynamical systems to this KdV equation, we have presented the existence of two types of traveling wave solutions which are solitary wave solutions and periodic traveling wave solutions. Under different parametric conditions, some exact explicit solutions of the above waves are obtained.     

Kepler’s celestial two-body equation: a second attempt to establish a continuous and integrable solution via the <Emphasis Type="Italic">BPES</Emphasis>: Boubaker Polynomials Expansion Scheme

The propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ions, and nonthermal electrons is studied. By using the reductive perturbation theory, the Kadomtsev–Petviashivili (KP) equation is derived. The energy of the soliton has been calculated. By using standard normal modes analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the energy of the soliton and the angular frequency of the linear wave are also discussed. It is shown that the amplitude of solitary waves of the KP equation diverges at the critical values of plasma parameters. We derive solitons of a modified KP equation with finite amplitude in this situation.     

Electrostatic solitons in rotating dusty plasmas with anisotropic ion pressure

The Zakharov-Kuznetsov (ZK) equation is derived for electrostatic wave in a rotating magnetoplasma with anisotropic ion pressure and in the presence of stationary charged dust particles. The anisotropic ion pressure is defined using double adiabatic Chew-Golberger-Low (CGL) theory. The reductive perturbation method is employed to study the dynamics of obliquely propagating low frequency ion acoustic wave with adiabatic ions. It is found that the ion pressure anisotropy, polarity, density of the dust particles and rotational frequency have significant effects on the formation nonlinear structures in rotating magnetized dusty plasmas. The numerical results are also presented for illustration.     

Obliquely propagating electrostatistic solitary structures in a hot magnetized dusty plasma with vortex-like electron distribution

The nonlinear properties of solitary waves structure in a hot magnetized dusty plasma consisting of a negatively charged, extremely massive hot dust fluid, positively charged hot ion fluid and vortex-like distributed electrons, are reported. A modified Korteweg de Vries equation (mKdV) which admits a solitary wave solution for small but finite amplitude is derived using a reductive perturbation theory. The modifications in the amplitude and width of the solitary wave structures due to the inclusion of an external magnetic field and dust and ions temperature are investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with nonextensive ions

Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with q-nonextensive velocity distributed ions are studied through non-perturbative approach. Basic equations are reduced to an ordinary differential equation involving electrostatic potential. After that by applying the bifurcation theory of planar dynamical systems to this equation, we have proved the existence of solitary wave solutions and periodic wave solutions. Two exact solutions of the above waves are derived depending on the parameters. From the solitary wave solution and periodic wave solution, the effect of the parameter (q) is studied on characteristics of dust acoustic solitary waves and periodic waves. The parameter (q) significantly influence the characteristics of dust acoustic solitary and periodic structures.     

Nonplanar Ion Acoustic Waves with Nonthermal Electrons

Using the standard reductive perturbation technique, nonlinear cylindrical and spherical Kadomtsev-Petviashvili (KP) equations are derived for the propagation of ion acoustic solitary waves in an unmagnetized collisionless plasma with nonthermal electrons and warm ions. The influence of nonthermally distributed electrons and the effects caused by the transverse perturbation on cylindrical and spherical ion acoustic waves (IAWs) are investigated. It is observed that the presence of nonthermally distributed electrons has a significant role in the nature of ion acoustic waves. In particular, when the nonthermal distribution parameter ?? takes certain values the usual cylindrical KP equation (CKPE) and spherical KP equation (SKPE) become invalid. One then has to have recourse to the modified CKPE or SKPE. Analytical solutions of both CKPE and SKPE and their modified versions are discussed in the present paper. The present investigation may have relevance in the study of propagation of IAWs in space and laboratory plasmas.     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

Detection of ionospheric perturbation due to a soft gamma ray repeater SGR J1550-5418 by very low frequency radio waves

The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.     

Compressive and Rarefactive Dust-acoustic Solitary Structures in a Magnetized Two-ion-temperature Dusty Plasma

A rigorous theoretical investigation has been made of obliquely propagating dust-acoustic solitary structures in a cold magnetized two-ion-temperature dusty plasma consisting of a negatively charged, extremely massive, cold dust fluid and ions of two different temperatures. The reductive perturbation method has been employed to derive the Korteweg-de Vries (K-dV) equation which admits a solitary wave solution for small but finite amplitude limit. It has been shown that the presence of second component of ions modifies the nature of dust-acoustic solitary structures and may allow rarefactive dust-acoustic solitary waves (solitary waves with density dip) to exist in such a dusty plasma system. The effects of obliqueness and external magnetic field on the properties of these dust-acoustic solitary structures are also briefly discussed.     

Formation of obliquely propagating dust-ion-acoustic shock waves due to dust charge fluctuation in magnetized nonthermal dusty plasma

A theoretical investigation is made on the formation as well as basic properties of dust-ion-acoustic (DIA) shock waves in a magnetized nonthermal dusty plasma consisting of immobile charge fluctuating dust, inertial ion fluid and nonthermal electrons. The reductive perturbation method is employed to derive the Korteweg-de Vries-Burgers equation governing the DIA shock waves. The combined effects of external static magnetic field, obliqueness, nonthermal electron distribution and dust charge fluctuation on the DIA shock waves are also investigated. It is shown that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the DIA shock waves. It is also observed that the combined effects of obliqueness, nonthermal electron distribution and dust charge fluctuation significantly modify the basic properties of the DIA shock waves. The implications of our results in space and laboratory dusty plasma situations are briefly discussed.     

On the Characteristics of Wave Propagation in a Magnetized Dusty Plasma with Streaming of Electrons and Ions

Propagation of waves in a magnetized dusty plasma are studied for all the range of values of ion-cyclotron frequency, and having streams of electrons and ions. The dispersion relation is obtained for the waves propagating through the dusty plasma and analysed for different modes of propagation for relative abundance of dust in the plasma. It is observed that abundance of dust, streaming motions of electrons and ions have an important influence on the propagation of waves in the dusty plasma particularly when the phase velocity of the wave is in the low frequency region. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonlinear propagation of dust-acoustic waves in a magnetized nonextensive dusty plasma

A theoretical investigation has been made of obliquely propagating dust-acoustic solitary waves in a magnetized three-component dusty plasma, which consists of a negatively charged dust fluid, ions, and nonextensive electrons. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits a solitary wave solution. It has been shown that the combined effects of external magnetic field (obliqueness), ions, and electron nonextensivity change the behavior of these electrostatic solitary structures that have been found to exist with positive and negative potential in this dusty plasma model. The implications of our results in astrophysical and cosmological scenarios like vicinity of the Moon, magnetospheres of Jupiter and Saturn, dark-matter halos, hadronic matter, quark-gluon plasma, protoneutron stars, stellar polytropes etc. have been mentioned.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.     

Bifurcations of ion acoustic solitary waves and periodic waves in an unmagnetized plasma with kappa distributed multi-temperature electrons

Ion acoustic solitary waves and periodic waves in an unmagnetized plasma with superthermal (kappa distributed) cool and hot electrons have been investigated using non-perturbative approach. We have transformed basic model equations to an ordinary differential equation involving electrostatic potential. Then we have applied the bifurcation theory of planar dynamical systems to the obtained equation and we have proved the existence of solitary wave solutions and periodic wave solutions. We have derived two exact solutions of solitary and periodic waves depending on the parameters. From the solitary wave solution and periodic wave solution, we have shown the effects of density ratio p of cool electrons and ions, spectral index κ, and temperature ratio σ of cool electrons and hot electrons on characteristics of ion acoustic solitary and periodic waves.     

Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized dusty electronegative plasma with trapped negative ions

A theoretical investigation has been made on obliquely propagating dust-ion-acoustic solitary waves (DIASWs) in magnetized dusty electronegative plasma containing Boltzmann electrons, trapped negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The reductive perturbation method has been employed to derive the modified Zakharov-Kuznetsov (MZK) equation which admits solitary wave solution under certain conditions. The multi-dimensional instability of these solitary waves is also studied by the small-k (long wavelength plane wave) perturbation-expansion technique. The basic properties (speed, amplitude, width, instability, etc.) of small but finite amplitude DIASWs are significantly modified by the effects of external magnetic field, obliqueness, polarity of dust, and trapped negative ions. The implications of our results in space and laboratory plasmas are briefly discussed.     

Evolution of ion-acoustic solitary waves in magnetized plasma contaminated with varying dust charged grains

Propagation of plasma-acoustic wave has been studied in magnetized plasma contaminated with dust charged grains. It has shown that, because of the configuration of magnetized plasma contaminated with dust charge fluctuation, pseudopotential method fails to derive nonlinear wave equation. We thus exercise an alternate approach to yield wave equation in the form of Sagdeev-like potential equation which enables the success to study the nonlinear waves. Again a modified mathematical formalism known as tanh-method has the merit to evaluate the soliton features in relation to its expectation in space. The method has its success in finding the solitary waves along with other exciting formation of shock-like wave, soliton radiation in soliton propagation. The results have more realistic interpretation in showing explicitly the interaction of magnetic field and impurity caused by dust charge variation.     

Higher-order Zakharov–Kuznetsov equation for dust-acoustic solitary waves with dust size distribution

Nonlinear propagating dust-acoustic solitary waves (DASWs) in a warm magnetized dusty plasma containing different size and mass negatively charged dust particles, isothermal electrons, high- and low-temperature ions are investigated. For this purpose, a reasonable normalization of the hydrodynamic and Poisson equations is used to derive the Zakharov–Kuznetsov (ZK) equation for the first-order perturbed potential. As the wave amplitude increases, the width and the velocity of the solitons deviate from the prediction of the ZK equation, i.e., the breakdown of the ZK approximation. To describe the soliton of larger amplitude, a linear inhomogeneous Zakharov-Kuznetsov-type (ZK-type) equation for the second-order perturbed potential is derived. Stationary solutions of both equations are obtained using the renormalization method. Numerically, the effect of power law distribution on the higher-order corrections is examined. It is found that the soliton amplitude in case of power law distribution is smaller than that of monosized dust grains. The higher-order corrections play a role to reduce the strength of the nonlinearity for power law distribution case. The relevance of the present investigation to Saturn's F-ring and laboratory experiment is discussed.