The spectacular Supernova SN1987A: Grain evaporation and condensation

Non-similarity solutions of the equations governing the motion of a perfect gas behind a cylindrical shock wave of variable strength have been obtained. These solutions are applicable to both the weak and the strong shocks. The nature of flow and field variables are illustrated through graphs. The total energy of the wave is taken to be constant.     

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.     

A new shock locus for similarity solutions in one-dimensional unsteady gas dynamics

This paper deals with shock conditions for the progressing wave (or similarity) solutions of one-dimensional, unsteady gas dynamics. These solutions have hitherto been used to deal with the flow behind shocks moving into stationary atmospheres. By generalising the shock conditions to the case of moving atmospheres, it is shown that the progressing wave solutions can be used to describe a certain class of flows, and a new shock locus can be constructed in the phase plane of the solutions. It is hoped that such solutions will be of use in describing the unsteady flow behind shocks propagating into the ambient solar wind.     

Bifurcations of dust ion acoustic travelling waves in a magnetized quantum dusty plasma

Bifurcation behavior of nonlinear dust ion acoustic travelling waves in a magnetized quantum dusty plasma has been studied. Applying the reductive perturbation technique (RPT), we have derived a Kadomtsev-Petviashili (KP) equation for dust ion acoustic waves (DIAWs) in a magnetized quantum dusty plasma. By using the bifurcation theory of planar dynamical systems to the KP equation, we have proved that our model has solitary wave solutions and periodic travelling wave solutions. We have derived two exact explicit solutions of the above travelling waves depending on different parameters.     

Self-similar magnetogasdynamic cylindrical shock waves,I

Similarity solutions describing the flow of a perfect gas behind a cylindrical shock wave with transverse magnetic field are investigated in an inhomogeneous medium. The total energy of the shock wave is assumed to be constant. A comparative study has been made between the results with and without magnetic field.     

Solitons and other solutions to the quantum Zakharov-Kuznetsov equation

In this paper, we present G′/G-expansion method, exp-function method, modified F-expansion method as well as the traveling wave hypothesis for finding the exact traveling wave solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas. By these methods, rich families of exact solutions have been obtained, including soliton solutions. This work continues to reinforce the idea that the proposed methods, with the help of symbolic computation, provide a powerful mathematical tool for solving nonlinear partial differential equations.     

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.     

Global shearing modes of galactic disks

A new scheme has been devised to calculate discrete unstable global shearing spiral modes of gaseous disk models of galaxies. The scheme makes use of the Legendre expansion of eigen functions and the problem of stability analysis is reduced to an eigenvalue problem of an infinite matrix. The spiral patterns of these shearing wave solutions of linearized equations change their form in the course of time due to the differential rotation of the equilibrium disk. These shearing wave solutions are presumed to have intermediate characteristics between so-called density-waves and material arms. Comparison between these shearing modes and the non-shearing normal modes for a series of disk models is presented.     

Massive scalar field interacting with viscous fluid distribution in cosmological models

The study of Einstein's field equations describing Robertson-Walker cosmological models with massive scalar field and viscous fluid representing the matter has been made. The problem has been investigated with and without the source density in the wave equation. Corresponding exact solutions of the field equations have been obtained under different physical equations of state: namely, (i) dust distribution, (ii) Zeldovich fluid distribution, (iii) disordered distribution of radiation subject to physically realistic conditions. The physical interpretations of the physically realistic solutions has been investigated. It has been found that physically realistic solutions has been obtained for closed cosmological models only.     

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.     

Finite Larmor radius effects on the Rayleigh-Taylor instability of a rotating plasma of variable density

The Rayleigh-Taylor instability in a rotating plasma of variable density has been investigated to include simultaneously the effects of viscosity and the finiteness of the ion Larmor radius. It is shown that, for a plasma in which the density is stratified along the vertical, the solution is characterized by a variational principle. Making use of this, proper solutions have been otained for a semiinfinite plasma in which the density varies exponentially. The dispersion relation has been solved numerically and it is found that the influence of the effects of both FLR and viscosity is stabilizing. The Coriolis forces are found to have a dual role, stabilizing for small wave numbers and destabilizing for large wave numbers. The range of the small wave numbers, over which the Coriolis forces have a stabilizing influence, is found to increase with Coriolis forces.     

Force-free electromagnetic waves

The time-dependent Force-Free Electromagnetic Field (FFEMF) is studied. In contrast to the case of Force-Free Magnetic Field (FFMF), it is shown that the FFEMF can occur in the form of waves. The FFEMF wave equation is solved in the case of one spatial dimension. Besides a periodical linear FFEMF wave solutions, the existence of solitary wave solutions is demonstrated. The possible application of FFEMF solutions to solar flares is discussed.Work done at the Space Environment Laboratory, NOAA/ERL/SEL, Boulder, CO 80303, U.S.A.     

Self-similar strong shock waves with thermal radiation in an atmosphere of exponentially-decreasing density

Similarity solutions describing the flow of a perfect gas behind a strong plane shock wave propagating in an exponentially decreasing atmosphere with radiation heat flux are investigated. The Planck's diffusion approximation has been taken into account to observe the effects of radiation heat flux.     

Product spaceV 2xV 2 and plane fronted waves in general projective relativity

In this paper the field equations of General Projective Relativity have been investigated in the product space ofV ₂xV ₂ space-time (Bertotti, 1959) and plane fronted metric of Peres (1959). It is shown that wave solutions exist in both space-times. In Peres' space we mention two solutions which can be interpreted as plane-monochromatic waves and wave packets, respectively.     

An isothermal shock wave in a perfectly-conducting and non-homogeneous stellar interior

In the present paper, we have obtained some exact analytic self-similar solutions for a zero-temperature gradient behind a magnetogasdynamic shock wave produced by stellar explosions. The initial density of the medium is taken to vary as some power of the distance from the point of explosion. The solutions are obtained for the cases when the energy of the shocked gas is constant, the energy is varying, and the shock velocity is constant. General solutions are also obtained. We have also analytically obtained the position of the singular surface behind the shock wave.     

Self-similar cylindrical shock waves with radiation heat flux

Similarity solutions describing the flow of a perfect gas behind cylindrical shock waves with radiation heat flux are investigated. The total energy of the expanding wave has been supposed to remain constant. The solution, however, is only applicable to a gaseous medium where the undisturbed pressure falls as the inverse square of the distance from the line of explosion.     

Magnetogasdynamic cylindrical shock wave model in an optically thin atmosphere

Similarity solutions for one-dimensional unsteady isothermal flow of a perfect gas behind a magnetogasdynamic shock wave including the effects of thermal radiation has been investigated in a uniform thin atmosphere. The flow is caused by an expanding piston and the total energy of the flow is assumed to be constant. Radiation pressure and energy have been neglected in comparison to radiation heat flux and the gas is assumed to be grey and opaque.     

Similarity solutions for an axially symmetric explosion model in magnetogasdynamics. I

Similarity solutions, for a point explosion in a spheroid with axially symmetric density distribution obeying power laws in the presence of magnetic field, are obtained. A new technique suggested by Bhowmick (1978) has been utilised to study the character of flow variables behind the shock front in an axisymmetric model. The total energy of the wave is constant.     

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.     

An explosion in non-ideal gas with magnetic field,II

Similarity solutions for a point explosion in a non-ideal gas, are investigated in the presence of magnetic field. The shock ahead of the point explosion is assumed to be strong. The energy of the expanding wave has been assumed to be time-dependent obeying a power law. The equation of state in the suitable form for such gases is found to be fairly accurate at low density region.