G. Pakira

Dissipative formation of hole-like excitation in ion-acoustic plasma

A viscous plasma is analyzed by reductive perturbation theory to model dissipative soliton formation. A nonlinear Schrödinger equation with complex coefficients is derived. Such an equation can be exactly solved by the technique due to Hirota. Three types of solution can be obtained under different physical conditions: solitary waves, ion-acoustic holes, and shocks. Even in the presence of a dissipative effect like viscosity, it is possible to obtain a solitary-wave-like excitation.

On the envelope soliton near critical density in a plasma with cold ions and two-temperature electrons

SummaryWe have analysed the formation of envelope soliton near critical density in a plasma consisting of two-temperature electrons and cold ions. The non-linear Schrödinger-like equation obtained isiφt+pφxx+q|φ|4φ=0 which we call the modified non-linear Schrödinger equation. It is also observed that this approach leads to a physical situation where a linear combination of both the modified and usual NLS equations holds, in the formiφt+pφxx+q1|φ|2φ +q2|φ|4φ=0. It is demonstrated through graphical analysis thatq1,q2, thought of as a function of β(=Tel/Teh), behave in opposite way. That is, whenq1 grows,q2 decays, or vice versa. Lastly we demonstrate that this equation can sustain a type of solution other than the usual solitary profile. The form of such a wave is also depicted graphically.

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 ion-acoustic soliton in a relativistic beam ion plasma system

The authors analyzed the formation of ion-acoustic solitons in a beam-plasma system, where both the beam and the ion were considered to be relativistic. The system is assumed to be nonisothermal. Both lower- and higher-order computations are performed, and the change of the wave profile is discussed, both in the lower and higher order. It is observed that both the amplitude and the width of the soliton change significantly in the presence of the relativistic effect and ion beam. The variations of these quantities with respect to v/sub 0//c, the ion-beam population, and the nonisothermality of the plasma are depicted graphically and compared with other results. >

Nonlinear wave number shift and modulational instability for large amplitude waves in a relativistic magnetised plasma

Properties of large amplitude waves in a relativistic magnetised plasma are studied using the method of reductive perturbation. The plasma under consideration consists of warm adiabatic ions and isothermal warm electrons, under the influence of a magnetic field. A onsideration of large amplitude waves demands study of the relativistic situation. In the present case we consider both the electrons and ions to be relativistic. A KdV equation is derived from which a nonlinear Schrodinger equation is deduced by further scaling. Lastly we derive an expression for nonlinear wave number shift, critical angle of propagation and the condition for modulational instability. Our analysis is applicable to both laboratory and space plasmas.

Effect of electron-ion collision on the ion-acoustic solitary wave in a relativistic plasma

SummaryWe have considered the effect of electron-ion collision on the structure of the solitary wave in a relativistic unmagnetized plasma. In the present analysis we have considered ions to be cold, the electrons hot. The equation obtained for ion velocity is not the usual KdV type but a perturbed version of it, where the perturbing term is proportional to the electron-ion collision frequency. Lastly we have used the method of Bogoliubov-Mitropolsky to study the change in the solitary-wave profile due to this perturbation.

On a kinetic approach to the modulational stability of envelope solitons in a relativistic plasma in an external electric field

SummaryThe formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field. We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration.