Modulation of the Nonlinear Ion Acoustic Waves in a Weakly Relativistic Warm Plasma with Nonextensively Distributed Electrons

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 Schrödinger-type (NST) equation for finite wavenumber 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.

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

“…Equation (4) is a generalized cubic‐quintic NLS equation with cubic derivative terms. It is known to govern the propagation of ultrashort pulses in a single‐mode optical fiber, [ 47 ] the modulations of weakly nonlinear ions in acoustic plasma waves, [ 48 ] ferromagnetic chain, [ 49 ] evolutions of Stokes waves, [ 50 ] soliton propagation in optical fibers, and metamaterials, [ 51,52 ] etc. Equation (4) can also be applied to the description of high‐intensity pulse propagation, [ 53 ] controllable self‐steepening, [ 54 ] and generation of Cherenkov radiation [ 55 ] in quadratic crystals.…”