K. Roy Chowdhury

Effect of electron inertia on double layers in a relativistic hot plasma

The ion-acoustic double layer in a relativistic hot plasma is studied by considering the effect of electron inertia. The critical region is analysed with the help of a combination of the KdV and mKdV equations obtained via a reductive perturbation technique. The profiles of the double layer are explicitly obtained for various values of the plasma parameters and of the electron-ion mass ratio.

Higher-order corrections to solitary waves in a non-isothermal relativistic plasma with cold ions and two-temperature electrons

A critical analysis of nonlinear waves in a non-isothermal relativistic plasma is performed using reductive perturbation theory. The plasma is assumed to contain two-temperature electrons. Higher-order corrections to the solitary wave are also computed, and the variations of the profile with respect to v / c , the two temperatures of the electrons, and the parameters b l , and b n characterising the non-isothermal nature are depicted graphically and com-pared with previous results.

On the modulation of ion-acoustic solitary waves in a cylindrical warm plasma near critical density

SummaryWe have derived a modified cylindrical K-dV (MCK-dV) equation for an ion-acoustic wave in a warm plasma with two-temperature electrons, in a cylindrical geometry, near the critical density where the nonlinearity of the usual CK-dV vanishes. The solitary-wave solution of MCK-dV is then discussed analytically using the concept of adiabatic invariants and the basic theorem due to Lax, instead of any numerical evaluation. This modulated form of the solitary wave is then discussed graphically as regards its variation with respect to the change in concentration of law- and high-temperature electrons.

Lie-Bäcklund transformation and ordinary differential equations associated with some nonlinear equations

Lie-Bäcklund-type analysis have been performed for one nonlinear partial differential equation, which is somewhat different from those usually studied. We consider the KdV equation with an explicit x dependence. In this case we show the form of symmetry generators and find the ordinary differential equation connected with them having no movable critical points. This clearly extends the class of equations analysed by Ablowitz.

On the generation of magnetic fields due to ponderomotive forces in astrophysical plasmas

The generation of magnetic fields due to ponderomotive forces in astrophysical plasma consisting of electrons, ions and positrons is investigated theoretically. It is seen that collisional or non-collisional interactions (between electromagnetic waves and plasma particles) via ponderomotive forces in an inhomogeneous plasma can excite a magnetic field. The growth rate of the magnetic field is illustrated graphically for different values of the temperature and concentration of positrons in the plasma.

Nonlinear equation in (2+1) dimensions for a plasma with negative ions

A new form of coupled nonlinear evolution equation is derived for a plasma with negative ions in (2+1) dimensions. This system of equations can be considered to be an extension of the usual Davey–Stewartson equation. A modified version of reductive perturbation has been used. It is also shown that this set of equations can sustain both cnoidal type and the usual solitary wave-like solution. Such an equation can have important applications in describing nonlinear wave propagation in a dusty plasma.

Effect of streaming and finite geometry on a resonance-like phenomenon in beam-plasma systems

We have analysed the effect of finite geometry and streaming on a resonance-like phenomenon in a beam-plasma system placed in an infinite magentic field. The resonance-like phenomenon is displayed through a variation of the amplitude of the soliton with respect to a (the ratio of electron to ion density). It is shown that this event is very prominent in the case of an infinite plasma, but for a bounded system the effect is not so significant. As such, an effect of this type will be difficult to observe experimentally unless the dimension of the containment system is considerable. Furthermore, the peak of the resonance varies considerably with the streaming velocity and other parameters of the plasma. The whole phenomenon is crucially dependent on the phase velocity of the solitary wave, whose variation is also considered in detail. Lastly, it is demonstrated that the existence of a resonance-like phenomenon can also be ascertained from an analysis of the linear dispersion relation.

On the envelope solitons in a relativistic ion-acoustic plasma

Nonlinear Schrodinger equation describing the envelope solitons is deduced in the case of ion-acoustic relativistic plasma, without taking recourse to the usual reductive perturbation theory. The methodology is that of Fried et al. (1973), which in some sense can be considered to be an extension of the effective (pseudo) potential theory. Amplitude and velocity of the solitary wave are obtained in terms of the physical parameters of plasma.

Lie Symmetry, Rational Solution and Bilinear Operator Structure for One and Two Dimensional Nonlinear Equations

We have systematized and extended the technique of Sym for obtaining the rational solutions of nonlinear equations in one and two space dimension through the use of Lie Symmetry and Hirotas bilinear operator, our method is easily extensible for higher dimensional integrable equations.