Cylindrical KP-Burgers Equation for Two-Temperature Ions in Dusty Plasma with Dissipative Effects and Transverse Perturbations

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unrsagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coeiffcient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effecta of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

Stability of a Composite Wave of Two Viscous Shock Waves for the Full Compressible Navier-Stokes Equation

In this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full compressible Navier-Stokes equation. By introducing a new linear diffusion wave special to this case, we successfully prove that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which are not necessarily of zero integral are suitably small, the unique global solution in time to the full compressible Navier-Stokes equation exists and asymptotically tends toward the corresponding composite wave whose shifts (in space) of two viscous shock waves are uniquely determined by the initial perturbations. We then apply the idea to study a half space problem for the full compressible Navier-Stokes equation and obtain a similar result. Research is supported in part by NSFC Grant No. 10471138, NSFC-NSAF Grant No. 10676037 and 973 project of China, Grant No. 2006CB805902, in part by Japan Society for the Promotion of Science, the Invitation Fellowship for Research in Japan (Short-Term). Research is supported in part by Grant-in-Aid for Scientific Research (B) 19340037, Japan.     

部分填充手征等离子体波导的电磁波

 把麦克斯韦方程和电磁场分解成横向和纵向分量, 导出了简明的一般性的手征等离子体填充的任意截面波导的波动方程和横向纵向场的关系式。对于部分填充手征等离子体波导, 导出了它的色散方程。这一方程的数值解给出了HE₁₁, EH₀₁和HE₂₁模式的色散图。随着手征等离子体填充面积的增大, EH₀₁模式的色散曲线向更高的频率移动。随着手征导纳的增加, 传播常数减小。     

Kadomtsev-Petviashvili (KP) Burgers equation in a dusty plasmas with non-adiabatic dust charge fluctuation

The nonlinear dust acoustic waves in a dusty plasmas with the combined effects of non-adiabatic dust charge fluctuation and higher-order transverse perturbation are studied. Using the perturbation method, a Kadomtsev-Petviashvili (KP) Burgers equation that governing the dust acoustic waves is deduced for the first time. A particular solution of this KP Burgers equation is also obtained. It is show that the dust acoustic shock waves can exist in the KP Burgers equation.Received: 18 March 2003, Published online: 15 July 2003PACS: 52.35.Sb Solitons; BGK modes - 52.35.Mw Nonlinear phenomena: waves, and nonlinear wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)     

On the neutral stability of a shock wave in real media

The results of the theoretical analysis and computer simulation of the behavior of neutrally stable shock waves with real (van der Waals gas, magnesium) equations of state are presented. An approach is developed in which the region of the neutral stability of a shock wave for each pressure value in front of the wave is determined from the analysis of the equation of state. A simple algorithm is developed to determine the cause of acoustic perturbations (a shock front or an external source) immediately from the flow pattern. In contrast to the predictions of the linear theory, the amplitude of the perturbations of the neutrally stable shock wave decreases with time, although this process is noticeably slower than in the case of an absolutely stable shock wave.     

Electron transport and permittivity in a plasma with an arbitrary ionic charge

Based on the solution of a linearized kinetic equation for electrons with a Landau collision integral, we develop a theory of electron transport for small perturbations in a completely ionized plasma with an arbitrary ionic charge that is free from any constraints on the characteristic perturbation time and length scales. We calculate the potential and vortex electron fluxes for an arbitrary electron collision frequency that allow the spatial and temporal nonlocal transport to be described. We also derive expressions for the longitudinal and transverse electron permittivities of a collisional plasma with an arbitrary ionic charge that are suitable for describing the plasma response to small perturbations with an arbitrary frequency and wave vector. Using the transverse permittivity, which allows the absorption of an electromagnetic wave to be described in the entire range of plasma parameters (from the strongly collisional to the collisionless one), as an example, we provide a detailed comparison with previously known models.     

Stability of shock waves for the Broadwell equations

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing the solution as the sum of a shock wave, a diffusive wave, a linear hyperbolic wave and an error term. The diffusive and linear hyperbolic waves are approximate solutions of the fluid dynamic equations corresponding to the Broadwell model. The error term is estimated using a variation of the energy estimates of Kawashima and Matsumura [6] and the characteristic energy method of Liu [7].Research supported by the Office of Naval Research through grant N00014-81-0002 and by the National Science Foundation through grant NSF-MCS-83-01260Research supported by the National Science Foundation through grant DMS-84-01355     

Reverse undercompressive shock structures in driven thin film flow

We show experimental and computational evidence of a new structure: an undercompressive and reverse undercompressive shock for draining films driven by a surface tension gradient against gravity. The reverse undercompressive shock is unstable to transverse perturbations while the leading undercompressive shock is stable. Depending on the pinch-off film thickness, as controlled by the meniscus, either a trailing rarefaction wave or a compressive shock separates from the reverse undercompressive shock.     

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.     

Cylindrical magnetoacoustic solitons in plasma

Nonlinear cylindrical magnetoacoustic perturbations in a plasma are considered in the framework of the two-liquid collisionless electromagnetic model. The method of power expansion in a small parameter in extended space-time coordinates is used to obtain the cylindrical Korteweg-de Vries equation that describes nonlinear radial cylindrical waves. An approximate solution to this equation has the form of a cylindrical magnetoacoustic compression soliton.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

The KP and ZK equations for electrostatic waves with grain charge fluctuation

The propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in unmagnetized/magnetized dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. The grain charge fluctuation effect is also incorporated through the current balance equation. By using the perturbation method, a Kadomtsev－Petviashvili equation and a Zakharov－Kuznetsov equation governing the nonlinear waves in the unmagnetized and magnetized systems are obtained respectively. It has been shown that with the combined effects of grain charge fluctuation, the transverse perturbation, and the external magnetic field would modify the wave structures. Waves in those systems are unstable to the high-order long-wave perturbations.     

Gauge-strings on Einstein-Rosen background

The full coupled Einstein scalar gauge field equations are obtained together with the high-frequency perturbations on a cylindrical symmetric background. The vortex solution and the first order perturbations depend critically on the parameters of the model. In the static case, an exact solution of the vortex is found. In the nondiagonal case, an axial component of the gauge field is necessary in order to fulfil the energy equation.     

Shocks and Solitons in Ultradense Degenerate Electron-Positron-Ion Plasmas

The formation and propagation of shocks and solitons are investigated in anunmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger (dKdVB) equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar (cylindrical and spherical) geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.     

Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system

This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.     

Lower order three-dimensional Burgers equation having non-Maxwellian ions in dusty plasmas

The dust acoustic(DA) shock wave with dust charge fluctuations, non-Maxwellian ions, and non-isothermal electrons is studied theoretically. The perturbation technique is employed to derive the lower order three-dimensional(3D) Burgers equation, and shock wave solution is explored by the tan-hyperbolic method. The effects of flat trapped and trapped electron distributions in the presence of Maxwellian and non-Maxwellian ions on characteristics shock waves are observed. The temperature ratio of non-Maxwellian ion temperature and non-isothermal electron temperature is found to play an important role in forming the shock-like structure.     

Instability of Waves in Magnetized Vortex-Like Ion Distribution Dusty Plasmas

A modified Zakharov-Kuznetsov equation for small but finite dustic waces in a magnetized votex-like ion distribution dusty plasma is obtained in this paper.It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.     

Effects of double spectral electron distribution and polarization force on dust acoustic waves in a negative dusty plasma

The nonlinear features of dust acoustic waves (DAWs) propagating in a multicomponent dusty plasma with negative dust grains, Maxwellian ions, and double spectral electron distribution (DSED) are investigated. A Korteweg de Vries Burgers equation (KdVB) is derived in the presence of the polarization force using the reductive perturbation technique (RPT). In the absence of the dissipation effect, the bifurcation analysis is introduced and various types of solutions are obtained. One of these solutions is the rarefactive solitary wave solution. Additionally, in the presence of the dissipation effects, the tanh method is employed to find out the solution of KdVB equation. Both of the monotonic and the oscillatory shock structures are numerically investigated. It is found that the correlation between dissipation and dispersion terms participates strongly in creating the dust acoustic shock wave. The limit of the DSED to the Maxwell distribution is examined. The distortional effects in the profile of the shock wave that result by increasing the values of the flatness parameter, r, and the tail parameter, q, are investigated. In addition, it has been shown that the proportional increase in the value of the polarization parameter R enhances in both of the strength of the monotonic shock wave and the amplitude of the oscillatory shock wave. The effectiveness of non-Maxwellian distributions, like DSED, in several of plasma situations is discussed as well.     

Dissipative structure in interplanetary plasma

Dissipative structures in hot interplanetary plasma are considered, which are formed due to a resonance interaction of long-wave longitudinal perturbations with nonlinear Alfven waves propagating along the magnetic field. The form of the structures is found by averaging known solutions of the derivative Schrodinger equation over the fast field phase. It is established that the dissipative structures are shaped as smooth parts of the envelope of the magnetic field, and that they are shock wave trains separated by rotational discontinuities. An equation is found which describes the structure of rotational discontinuities, and a simple step-like solution is found which fits well the obtained structures. These solutions agree with observations of rotational discontinuities in interplanetary plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 104–108, August, 1991.