Stability of Self Similar Flows of Second Kind in the Neighbourhood of a Critical Point

Following method developed by Bhatnagar & Prasad, based on the investigations of Kulikovskii & Slobodkina, we study the stability of self-similar flows generated by the propagation of shock-wave in an inhomogeneous medium with density varying either exponentially or as a power of distance. Also we consider the shocks produced by impulsive load. We find that all these flows are stable in the neighbourhood of critical point, which is a saddle point of the system of differential equations governing the flow in its neighbourhood

Electron acoustic solitons in the Earth's magnetotail

International audienceSmall amplitude electron - acoustic solitons are studied in a magnetized plasma consisting of two types of electrons, namely cold electron beam and background plasma electrons and two temperature ion plasma. The analysis predicts rarefactive solitons. The model may provide a possible explanation for the perpendicular polarization of the low-frequency component of the broadband electrostatic noise observed in the Earth's magnetotail

Ion-Acoustic Solitons in Bi-Ion Dusty Plasma

The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg-de-Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compressi- on and rarefaction solitons depends continuously on the dust density. A modified Korteveg-de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of the dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.Comment: 17 pages, 5 figure

Solitary Dust--Acoustic Waves in a Plasma with Two-Temperature Ions and Distributed Grain Size

The propagation of weakly nonlinear dust--acoustic waves in a dusty plasma containing two ion species with different temperatures is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are derived. It is shown that the properties of dust--acoustic waves depend substantially on the grain size distribution. In particular, for solitary dust--acoustic waves with a positive potential to exist in a plasma with distributed grain size, it is necessary that the difference between the temperatures of two ion species be large that that in the case of unusized grains.Comment: 16 pages, 6 figure

On Propagation of One Dimensional Small Amplitude Waves in Radiating Viscous and Heat Conducting Gas

"In this paper, effect of radiation, heat-conduction and viscosity on propagation of one-dimensional small amplitude waves is investigated. It is shown that there are three distinct modes of propagation viz. (i) Radiation-induced mode, (ii) Modified gasdynamic mode and (iii) Coupled heat-conduction and viscous mode. The dispersion relation is solved both asymptotically and numerically. For very small values of omega, the asymptotic solution predicts the speed of propagation of distriubance as zero, as (isentropic sound velocity) and 0.336 times the isothermal sound velocity. For very large values of omega, the high frequency waves propagate with characteristic speeds of the seventh order operation.