Abstract
A reductive perturbation technique (multiple scales) is applied to a weakly relativistic warm unmagnetized adiabatic plasma system consisting of inertial ions fluid and nonextensively distributed electrons. A nonlinear Schrodinger-type (NST) equation for finite wave number at the second order is derived. Using the reductive perturbation technique we derived the corresponding Korteweg-de Vries (K-dV) equation. For small wavenumber limit the K-dV equation is transformed into NST equation. It is found that the coefficient of the NST equation obtained from the K-dV equation agree with the corresponding coefficients of NST equation obtained by the multiple scales. Moreover we investigated the effect of the physical parameters of the system namely temperature ratio of the ion temperature T_i to electron temperature T_e, the relativistic factor u_0/C as well as the nonextensive parameter (q) of the distribution on the stability/instability of the system. It is found that these parameters affect strongly on the stability/instability regions. Finally, the validity of our results in astrophysical plasma is briefly discussed.
Highlights
One of the basic wave processes in plasma is the ion acoustic waves (IAWs), which has been studied for several decades both theoretically and experimentally.[1,2,3,4,5,6,7] The first observation of ion acoustic solitons has been reported experimentally by Ikezi et al.[8]
We investigate the stability and instability regions of the ion acoustic waves for our plasma model on the basis of the NST equation (15)
We investigated the modulation of the nonlinear acoustic wave in a warm unmagnetized plasma consists of superthermal electrons and inertial adiabatic ions
Summary
One of the basic wave processes in plasma is the ion acoustic waves (IAWs), which has been studied for several decades both theoretically and experimentally.[1,2,3,4,5,6,7] The first observation of ion acoustic solitons has been reported experimentally by Ikezi et al.[8]. El-Labany[10] and El-Labany et al.[11] have been studied theoretically the modulation instability of IAWs for different distribution by using the multiple scales method. The distribution may arise due to the external forces acting on a wave particle interaction or the neutral space plasmas This distribution goes back to Maxwellian distribution for limit of large spectral index [18] i.e., There are different approximation techniques for describing the nonlinear evolutions in plasmas. Such as the multiple scales method [10,11], derivative expansion method [20] and Krylov-BogoliubovMitropolsky [21] method.
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