The Kadomtsev–Petviashvili (KP), MKP,and coupled KP equations for two-ion-temperature dusty plasmas

It is well known that the Korteweg–de Vires (KdV) equation can describe small but finite amplitude dust acoustic waves in a dusty plasmas. In this paper, we use the reductive perturbation method and derive a Kadomtsev–Petviashvili (KP) equation, a modified KP (MKP) equation and a coupled KP equation for unmagnetized, collisionless, cold, and two-ion-temperature dusty plasmas with N different species of dust grains. We find that if a solitary wave exist in this system, the smaller grains have larger velocities and propagate longer distances than that of larger particles. The comparisons are given between the dusty plasma composed by different dust particles and the mono-sized dusty plasma.     

3+1 dimensional envelop waves and its stability in magnetized dusty plasma

It is well known that there are envelope solitary waves in unmagnetized dusty plasmas which are described by a nonlinear Schrodinger equation (NLSE). A three dimension nonlinear Schrodinger equation for small but finite amplitude dust acoustic waves is first obtained for magnetized dusty plasma in this paper. It suggest that in magnetized dusty plasmas the envelope solitary waves exist. The modulational instability for three dimensional NLSE is studied as well. The regions of stability and instability are well determined in this paper.     

Envelop solitons in dusty plasmas for warm dust

A nonlinear Schrödinger equation is obtained for the warm dusty plasmas. The modulational instability of envelop soliton is investigated in this paper. Both the temperature of the dust grains and the charge variations of dust grains affect the instability regions of the dusty plasmas. It also affect the amplitude and the width of the envelop soliton.     

Theoretical results of the dust acoustic waves in a magnetized dusty plasma with different dust particles

In this paper, the nonlinear dust acoustic waves (DAW) in a magnetized dusty plasmas with different dust grains are analytically investigated. New analytical solutions of the governing equation for this system have been obtained for the first time. The exact mathematical expressions of the nonlinear dust waves have been canvassed for the general case in magnetized dusty plasma containing different dust particles.     

Propagation of the nonlinear damped Korteweg‐de Vries equation in an unmagnetized collisional dusty plasma via analytical mathematical methods

In this article, we consider the problem formulation of dust plasmas with positively charge, cold dust fluid with negatively charge, thermal electrons, ionized electrons, and immovable background neutral particles. We obtain the dust‐ion‐acoustic solitary waves (DIASWs) under nonmagnetized collision dusty plasma. By using the reductive perturbation technique, the nonlinear damped Korteweg‐de Vries (D‐KdV) equation is formulated. We found the solutions for nonlinear D‐KdV equation. The constructed solutions represent as bright solitons, dark solitons, kink wave and antikinks wave solitons, and periodic traveling waves. The physical interpretation of constructed solutions is represented by two‐ and three‐dimensional graphically models to understand the physical aspects of various behavior for DIASWs. These investigation prove that proposed techniques are more helpful, fruitful, powerful, and efficient to study analytically the other nonlinear nonlinear partial differential equations (PDEs) that arise in engineering, plasma physics, mathematical physics, and many other branches of applied sciences.     

The water bag model and gyrokinetic applications

Predicting turbulent transport in nearly collisionless fusion plasmas requires to solve kinetic (or more precisely gyrokinetic) equations. In spite of considerable progress, several pending issues remain; although more accurate, the kinetic calculation of turbulent transport is much more demanding in computer resources than fluid simulations. An alternative approach is based on a water bag representation of the distribution function which is not an approximation but rather a special class of initial conditions allowing to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations while keeping its kinetic character. This model has been applied to gyrokinetic modelling with very encouraging results. The instability threshold for ITG instability is found to be very close to the results obtained from continuous Maxwellian distribution, even for only 10 bags.     

Obliquely propagating dust-acoustic solitary waves in cosmic dust-laden plasmas

Obliquely dust-acoustic solitary waves in a collisional, magnetized dusty plasmas having cold dust grains, isothermal electrons, two temperature isothermal ions and stationary neutrals are studied via a reductive perturbation method. It is found that the effects of two temperature ions, collisions, magnetic field and directional cosine of the waves vector k along the x-axis have vital roles in the behavior of the dust acoustic solitary waves. The present investigation can be relevance to the electrostatic solitary structures observed in various cosmic dust-laden plasmas, such as Saturn’s E-ring, noctilucent clouds, Halley’s comet and interstellar molecular clouds.     

Convergence of domain decomposition methods via semi-classical calculus semiclassical calculus

We present a model hierarchy of hydrodynamic and quasihydrodynamic equations for plasmas consisting of electrons and ions, and give a rigorous proof of the zero-relaxation-time limits in the hydrodynamic equations. described by the Euler equations coupled with a linear or nonlinear Poisson equation. The proof is based on the high energy estimates for the Euler equations together with compactness arguments.     

Stagnation point flow of dusty Casson fluid with thermal radiation and buoyancy effects

The aim of the study is to examine the stagnation point flow of a dusty Casson fluid over a stretching sheet with thermal radiation and buoyancy effects. The governing boundary layer equations are represented by a system of partial differential equation. After applying suitable similarity transformations, the resulting boundary layer equations are solved numerically using the Runge Kutta Fehlberg fourth-fifth order method (RKF-45 method). The behaviors of velocity, temperature and concentration profiles of fluid and dusty particles with respect to change in fluid particle interaction parameter, Casson paramter, Grashof number, radiation parameter, Prandtl number, number density, thermal equilibrium time, relaxation time, specific heat of fluid and dusty particles, ratio of diffusion coefficients, Schmidt number and Eckert number are analysed graphically and discussed. Our computed results interpret that velocity distribution decays for higher estimation of Casson parameter while temperature distribution shows increasing behavior for larger radiation parameter.     

Global weak solutions to the cometary flow equation with a self-generated electric field

We study the Cauchy problem of a cometary flow equation with a self-generated electric field. This kinetic model originates from the theory of astrophysical plasmas and can be viewed as a perturbation, by a wave-particle collision operator, of the classical Vlasov-Poisson system. By asymptotic methods in kinetic theory, global existence of nonnegative weak solutions to the Cauchy problem in three space variables is established for bounded initial data having finite second order velocity moments.     

Higher order solution of the dust ion acoustic solitons in a warm dusty plasma with vortex-like electron distribution

The ratios of dust to free electron and free to trapped electron temperatures are examined in warm dusty plasmas with vortex-like electron distribution through the derivation of a modified Korteweg–de Vries (MKdV) equation using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the MKdV equation, i.e., the breakdown of the MKdV approximation. To describe the soliton of larger amplitude, the MKdV equation with the fifth-order dispersion term is employed and its higher-order solutions are obtained.     

Dust-acoustic solitary waves in a two-temperature electrons with charge fluctuations and nonisothermal ions

In this paper, a modified Korteweg–de Vries (mKdV) equation and Korteweg–de Vries (KdV) equation at critical ion density are derived for dusty plasmas consisting of hot dust fluid, nonisothermal ions and two-temperature electrons. The charge fluctuation dynamics of the dust grains has also been considered. It has been shown that the presence of a second component of electrons modifies the nature of dust acoustic (DA) solitary structures. The effects of two-temperature electrons, obliqueness and external magnetic field on the properties of DA solitary waves are discussed. Numerical investigations show that there exists only rarefactive solitary waves.     

Global existence and long-time behavior of smooth solutions of two-fluid Euler–Maxwell equations

We consider Cauchy problems and periodic problems for two-fluid compressible Euler–Maxwell equations arising in the modeling of magnetized plasmas. These equations are symmetrizable hyperbolic in the sense of Friedrichs but don?t satisfy the so-called Kawashima stability condition. For both problems, we prove the global existence and long-time behavior of smooth solutions near a given constant equilibrium state. As a byproduct, we obtain similar results for two-fluid compressible Euler–Poisson equations.     

Multidimensional dust acoustic solitary waves in inhomogeneous magnetized dusty plasmas with nonthermal ions

The linear dispersion relation and a modified variable coefficients Korteweg–de Vries (MKdV) equation governing the three-dimensional dust acoustic solitary waves are obtained in inhomogeneous dusty plasmas comprised of negatively charged dust grains of equal radii, Boltzmann distributed electrons and nonthermally distributed ions. The numerical results show that the inhomogeneity, the nonthermal ions, the external magnetic field and the collision have strong influence on the frequency and the nonlinear properties of dust acoustic solitary waves and both dust acoustic solitary holes (soliton with a density dip) and positive solitons (soliton with a density hump) are excited.     

Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas

Plasmas are believed to be possibly the most abundant form of ordinary matter in the Universe, supporting a variety of the wave phenomena, while a dusty plasma is of interest as a non-Hamiltonian system of interacting particles. In this Letter, symbolic computation on an observationally/experimentally-supported (2+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation is done, for certain dust-acoustic, electron-acoustic, positron-acoustic, magneto-acoustic, dust-magneto-acoustic, ion-acoustic, dust-ion-acoustic and/or quantum-dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. Auto-Bäcklund transformation and families of the solitonic solutions are obtained, for the electrostatic wave potential, perturbation of the magnitude of the magnetic field, fluctuation of electron or ion density, or radial-direction component of the velocity of ions or dust particles, relying on such plasma coefficient functions as the nonlinearity, dispersion, dusty-fluid-viscosity/Burgers-dissipation, geometric-effect and diffraction/transverse-perturbation coefficients. Shock structures presented in this Letter are very close to the experimental results previously reported. Future plasma observations/experiments might verify some other effects offered by our analytic results with respect to those plasma coefficient functions.     

Study of the dust acoustic waves in a magnetized dusty plasma with many different dust grains

The nonlinear dust waves in a magnetized dusty plasma with many different dust grains are analytically investigated. New analytical solutions for the governing equation of this system have been obtained for the dust acoustic waves in a dusty plasma for the first time. We derive exact mathematical expressions for the general case of the nonlinear dust waves in magnetized dusty plasma which contains different dust grains.     

Analyzing of the effect of the dusty fluid,anisotropy and layered of the wall on the wave propagation

This study considers the propagation of time harmonic waves in, prestressed, anisotropic elastic tubes filled with viscous fluid containing dusty particles. The fluid is assumed to be incompressible and Newtonian. The tube material is considered to be incompressible, anisotropic, and elastic. The tube is subjected to a static inner pressure P_i and an axial stretch λ. Utilizing the theory of “Superposing small deformations on large initial static deformations”, differential equations governing wave propagation inside the tube are obtained in terms of cylindrical coordinates. Analytical solutions for the equations of motion for the dust and the fluid are obtained, and expressed numerically. The dispersion relation is obtained as a function of the stretch, the thickness ratio and the parameters for dusty particles.     

Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations

The combined quasi-neutral and non-relativistic limit of compressible Navier-Stokes-Maxwell equations for plasmas is studied. For well-prepared initial data, it is shown that the smooth solution of compressible Navier-Stokes-Maxwell equations converges to the smooth solution of incompressible Navier-Stokes equations by introducing new modulated energy functional.     

Effects of the dust charge variation and non-thermal ions on multi-dimensional dust acoustic solitary structures in magnetized dusty plasmas

The combined effects of both adiabatic dust charge variation and non-thermally (fast) distributed ions on dust acoustic solitary structures are studied in a magnetized dusty plasmas consisting of the negatively and variably charged hot dust fluid, Boltzmann distributed electrons and non-thermally distributed ions. By using the reductive perturbation method, we derive the Korteweg-de Vries (KdV) equation governing the dust acoustic solitary waves. It is shown that the dust charge variation and the presence of non-thermally distributed ions would modify the nature of dust acoustic solitary structures significantly and may excite both dust acoustic solitary holes (soliton with a density dip) and positive solitons (soliton with a density hump).     

具量子效应Zakharov方程弱解的存在性

Zakharov方程具有丰富的物理背景．通过Arzela－Ascoli定理、Faedo－Galerkin方法和紧性原理,得到等离子体模型中具量子效应Zakharov方程弱整体解的存在性．