Dust-Acoustic Solitary Waves in an Unmagnetized Dusty Plasma with Arbitrarily Charged Dust Fluid and Trapped Ion Distribution

The nonlinear propagation of dust-acoustic (DA) solitary waves in three-component unmagnetized dusty plasma consisting of Maxwellian electrons, vortex-like (trapped) ions, and arbitrarily charged cold mobile dust grain has been investigated. It has been found that, owing to the departure from the Maxwellian ions distribution to a vortex-like one, the dynamics of small but finite amplitude DA waves is governed by a nonlinear equation of modified Korteweg-de Vries (mK-dV) type instead of K-dV. The reductive perturbation method has been employed to study the basic features (phase speed, amplitude, width, etc.) of DA solitary waves which are significantly modified by the presence of trapped ions. The implications of our results in space and laboratory plasmas are briefly discussed.

Modulated Dust-Acoustic Wave Packets in an Opposite Polarity Dusty Plasma System

The nonlinear propagation of the dust-acoustic bright and dark envelope solitons in an opposite polarity dusty plasma(OPDP) system(composed of non-extensive q-distributed electrons, iso-thermal ions, and positively as well as negatively charged warm dust) has been theoretically investigated. The reductive perturbation method(which is valid for a small, but finite amplitude limit) is employed to derive the nonlinear Schr¨odinger equation. Two types of modes, namely, fast and slow dust-acoustic(DA) modes, have been observed. The conditions for the modulational instability(MI) and its growth rate in the unstable regime of the DA waves are significantly modified by the effects of non-extensive electrons, dust mass, and temperatures of different plasma species, etc. The implications of the obtained results from our current investigation in space and laboratory OPDP medium are briefly discussed.

Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold （hot） dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

Dust Acoustic Solitary Waves in Saturn F-ring's Region

Effect of hot and cold dust charge on the propagation of dust-acoustic waves （DAWs） in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains has been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Kortewege-de Vries （KdV） equation. At the critical hot dusty plasma density Nho, the KdV equation is not appropriate for describing the system. Hence, a set of stretched coordinates is considered to derive the modified KdV equation. It is found that the presence of hot and cold dust charge grains not only significantly modifies the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical hot dusty plasma density Nho, neither KdV nor mKdV equation is appropriate for describing the DAWs. Therefore, a further modified KdV （fmKdV） equation is derived, which admits both soliton and double layer solutions.

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 dynamics of nonlinear propagation and interaction of the modified KP solitons in multicomponent complex plasmas

Dust-acoustic waves(DAWs)are analyzed in the small amplitude limit in a collisionless unmagnetized dusty plasma whose constituents are inertial dust grains,massless ions expressed by the generalized(r,q)distribution and inertialess Maxwellian electrons using the fluid theory of plasmas.The modified Kadomtsev-Petviashvili(mKP)equation is derived at a critical plasma condition for which the quadratic nonlinearity vanishes.The propagation of single soliton and interaction of two solitons are analyzed for the mKP equation in the context of plasma physics by employing Hirota bilinear formalism.The effects of the flatness parameter rand tail parameter q of the ions on the frequency of the DAWs are studied and the comparison with Maxwellian and kappa distributions is drawn.Using the plasma parameters corresponding to the Saturn’s E-ring,the range of electric field amplitude for dust-acoustic solitary waves(DASWs)for different ion distributions is calculated and is shown to agree very well with the Cassini Wideband Receiver(WBR)observations.The interaction time of two DASWs for non-Maxwellian ion distributions is estimated and shown to be fastest for the(r,q)distributed ions.The interesting feature of the interaction between compressive solitons with their rarefactive counterparts is also discussed in detail.

A New Approach to Energy Integral for Investigation of Dust-Ion Acoustic(DIA)Waves in Multi-Component Plasmas with Quantum Effects in Inertia Less Electrons

Dust-ion acoustic waves are investigated in this model of plasma consisting of negatively charged dusts, cold ions and inertia less quantum effected electrons with the help of a typical energy integral. In this case, a new technique is applied formulating a differential equation to establish the energy integral in case of multi-component plasmas which is not possible in general. Dust-ion acoustic （DIA） compressive and rarefactive, supersonic and subsonic solitons of various amplitudes are established. The consideration of smaller order nonlinearity in support of the newly established quantum plasma model is observed to generate small amplitude solitons at the decrease of Mach number. The growths of soliton amplitudes and potential depths are found more sensitive to the density of quantum electrons. The small density ratio r（= 1 - f） with a little quantized electrons supplemented by the dust charges Zu and the in-deterministic new quantum parameter C2 are found responsible to finally support the generation of small amplitude solitons admissible for the model.