Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons

The standard nonlinear Schrödinger Equation (NLSE) is one of the elegant equations to find detailed information about the modulational instability criteria of dust-ion-acoustic (DIA) waves and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium with inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that the plasma system supports both fast and slow DIA modes under consideration of inertial warm ions along with inertial negatively charged dust grains. It is also found that the modulationally stable parametric regime decreases with κ. The numerical analysis has also shown that the amplitude of the first and second-order DIARWs decreases with ion temperature. These results are to be considered the cornerstone for explaining the real puzzles in space and laboratory dusty plasmas.

Analytical Solitary Wave Solution of the Dust Ion Acoustic Waves for the Damped Forced Korteweg–de Vries Equation in Superthermal Plasmas

Analytical solitary wave solution of the dust ion acoustic (DIA) waves was studied in the framework of the damped forced Korteweg–de Vries (DFKdV) equation in superthermal collisional dusty plasmas. The reductive perturbation technique was applied to derive the DKdV equation. It is observed that both the rarefactive and compressive solitary wave solutions are possible for this plasma model. The effects of κ and the strength (f0) and frequency (ω) of the external periodic force were studied on the analytical solitary wave solution of the DIA waves. It is observed that the parameters κ, f0 and ω have significant effects on the structure of the damped forced DIA solitary waves. The results of this study may have relevance in laboratory plasmas as well as in space plasmas.

Weakly dissipative dust-ion acoustic wave modulation

The modulational instability of dust-ion acoustic (DIA) waves in an unmagnetized dusty plasma is investigated in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization recombination and ion loss. Based on the multiple space and time scales perturbation, a new modified nonlinear Schrödinger equation governing the evolution of modulated DIA waves is derived with a linear damping term. It is shown that the combined action of all dissipative mechanisms due to collisions between particles reveals the permitted maximum time for the occurrence of the modulational instability. The influence on the modulational instability regions of relevant physical parameters such as ion temperature, dust concentration, ionization, recombination and ion loss is numerically examined. It is also found that the recombination frequency controls the instability growth rate, whereas recombination and ion loss make the instability regions wider.

Effect of nonextensive electrons on dust–ion acoustic wave self-modulation

Nonlinear self-modulation of dust–ion acoustic (DIA) waves is studied in an unmagnetized dusty plasma comprising warm adiabatic ions, arbitrarily charged dust particles, and hot nonextensive q-distributed electrons. By employing the multiple space and time scales perturbation, a nonlinear Schrödinger equation is derived for the evolution of the wave amplitude. The existence along with the stability of wave packets are discussed in the parameter space of two oppositely charged dust and ion temperature over different ranges of the nonextensive parameter q. The growth rate of the modulation instability is also given for different values of the q parameter. It is found that the critical wave number at which the instability sets in increases as the nonextensive parameter q increases. This leads to a wider range (in spatial extension) of the stable envelope solitons. It is also found that the effects of ion temperature and negative (positive) dust concentration significantly modify the criteria for the modulation instability of DIA waves. Our finding should elucidate the nonlinear electrostatic structures that propagate in astrophysical and cosmological plasma scenarios where nonextensive particles exist: such as instellar plasma, stellar polytropes, cosmic radiation, and systems with long-rang interaction.

Nonplannar Nonlinear Dust ion Acoustics Solitary and Shock Waves in a Dusty Multi-ion Plasma

We have presented a stern theoretical exploration of the nonplannar and nonlinear propagation of dust-ion acoustic (DIA) waves in a dusty multi-ion plasma. We studied the progation of nonplannar non-linear DIA waves by the reductive perturbation method which leads to the the derivation of the Burgers [Korteweg de-Vries (K-dV)] equation for the shock (solitary) wave propagation. The shock (solitary) waves are found to be formed in a multi-ion dusty plasma due to the balance between nonlinearity and dissipation (dispersion), and that the dissipation (dispersion) arises due to the dust charge fluctuation (deviation of charge neutrality condition). We have analized the effects of nonplannar and nonlinear geometry on the DIA shock and solitary waves propagating in such a dusty multi-ion plasma. We have shown that the nonplanar (cylindrical and spherical) solitary and shock structures are significantly different from planner ones.

Compressive and rarefactive dust ion-acoustic solitary waves with degenerate electron–positron–ion plasma

The nonlinear propagation of dust ion-acoustic (DIA) waves in a unmagnetized collisionless degenerate dense plasma (containing degenerate electron and positron, and classical ion fluids) has been theoretically investigated. The K-dV equation has been derived by employing the reductive perturbation method and by taking into account the effect of different plasma parameters in plasma fluid. The stationary solitary wave solution of K-dV equation is obtained, and numerically analyzed to identify the basic properties of DIA solitary structures. It has been shown that depending on plasma parametric values, the degenerate plasma under consideration supports compressive or rarefactive solitary structures. It has been also found that the effect of pressures on electrons, ions, and positrons significantly modify the basic features of solitary waves that are found to exist in such a plasma system. The relevance of our results in astrophysical objects such as white dwarfs and neutron stars, which are of scientific interest, is discussed briefly.

Obliquely propagating dust–ion acoustic solitary waves and their multidimensional instabilities in magnetized dusty plasmas with bi-maxwellian electrons

The nonlinear propagation of dust–ion acoustic (DIA) waves in an obliquely propagating magnetized dusty plasma, consisting of bi-maxwellian electrons (namely lower and higher temperature maxwellian electrons), negatively charged immobile dust grains, and inertial ions is rigorously investigated by deriving the Zakharov–Kuznetsov equation. Later, the multidimensional instability of the DIA solitary waves (DIASWs) is analyzed using the small-k perturbation technique. It is investigated that the nature of the DIASWs, the instability criterion, and the growth rate of the perturbation mode are significantly modified by the external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes. The implications of the results obtained from this investigation in space and laboratory dusty plasmas are briefly discussed.

Sheared flow-driven vortices and solitary waves in a non-uniform plasma with negative ions and non-thermal distributed electrons

The coupled drift-ion acoustic (DIA) waves in an inhomogeneous magnetoplasma having negative and positive ions can be driven by the parallel sheared flows in the presence of Cairns distributed non-thermal electrons. The coupled DIA waves can become unstable due to shear flows. The conditions of modes instability are discussed with effects of non-thermal electrons. These are the excited modes and start interactions among themselves. The interaction is governed by the Hasegawa–Mima equations with analytical solutions in the form of a vortex chain and dipolar vortex. On the other hand, for scalar nonlinearity the Kortweg deVries-type equation is obtained with solitary wave solution. Possible application of the work to the space and laboratory plasmas are highlighted.

Cylindrical or spherical dust-ion acoustic soliton in an adiabatic dusty plasma with electrons following a q-nonextensive distribution

Using the reductive perturbation technique, a cylindrical and (or) spherical Korteweg – de Vries (KdV) equation is derived for a dust-ion acoustic solitary wave (DIASW) in an unmagnetized dusty plasma, whose constituents are adiabatic ion fluid, nonextensive electrons, and negatively charged static dust particles. The solution of the modified KdV equation in nonplanar geometry is numerically analyzed. The change of the DIASW structure due to the effect of the geometry, nonextensive parameter, dust density, and ion temperature is investigated by numerical calculation of the cylindrical and (or) spherical KdV equation. It is found that both compressive and rarefactive type DIA waves are obtained depending on the plasma parameter.