A Modified Reductive Perturbation Method as Applied to Nonlinear Ion-Acoustic Waves

1999 ◽  
Vol 68 (6) ◽  
pp. 1833-1837 ◽  
Author(s):  
Hilmi Dem\uiray
Keyword(s):  
Perturbation Method ◽  
Acoustic Waves ◽  
Reductive Perturbation Method ◽  
Ion Acoustic Waves ◽  
Reductive Perturbation ◽  
Ion Acoustic

Cylindrical ion-acoustic waves in a warm multicomponent plasma

2000 ◽  
Vol 63 (4) ◽  
pp. 343-353 ◽  
Author(s):  
S. K. EL-LABANY ◽  
S. A. EL-WARRAKI ◽  
W. M. MOSLEM
Keyword(s):  
Perturbation Theory ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Negative Ions ◽  
Ion Acoustic Waves ◽  
Multicomponent Plasma ◽  
Reductive Perturbation ◽  
Ion Acoustic ◽  
Ion Acoustic Solitons ◽  
Warm Plasma

Cylindrical ion-acoustic solitons are investigated in a warm plasma with negative ions and multiple-temperature electrons through the derivation of a cylindrical Korteweg–de Vries equation using a reductive perturbation theory. The results are compared with those for the corresponding planar solitons.

Nonlinear ion-acoustic waves in multicomponent plasmas

1988 ◽  
Vol 66 (1) ◽  
pp. 79-81 ◽  
Author(s):  
G. C. Das ◽  
B. Karmakar
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Perturbation Technique ◽  
Ionic Species ◽  
System Of Equations ◽  
Ion Acoustic Waves ◽  
Plasma Dynamics ◽  
Small Magnitude ◽  
Reductive Perturbation ◽  
Ion Acoustic

By applying the reductive perturbation technique to the basic system of equations governing plasma dynamics, a modified Korteweg–de Vries (KdV) equation is derived. The inclusion of nonisothermality, together with its reduction to a small magnitude, yields various interesting characteristics relating to the existence of solitons in multicomponent plasmas that include several ionic species and multiple nonisothermal electrons. The mathematical development shows that a closed relation among the solitons existing in the various plasmas arises due to the different magnitude of nonisothermalities.

Ion-acoustic shock waves in a degenerate dense plasma

2012 ◽  
Vol 79 (1) ◽  
pp. 65-68 ◽  
Author(s):  
M. S. ZOBAER ◽  
N. ROY ◽  
A. A. MAMUN
Keyword(s):  
Acoustic Waves ◽  
Dense Plasma ◽  
Reductive Perturbation Method ◽  
Nonlinear Propagation ◽  
Ion Acoustic Waves ◽  
Plasma System ◽  
Ion Acoustic ◽  
Astrophysical Objects ◽  
Basic Features ◽  
Ion Acoustic Shock Waves

AbstractA theoretical investigation on the nonlinear propagation of ion-acoustic waves in a degenerate dense plasma has been made by employing the reductive perturbation method. The Burger's equation has been derived, and numerically analyzed. The basic features of electrostatic shock structures have been examined. It has been shown that the plasma system under consideration supports the propagation of electrostatic shock structures. The implications of our results (obtained from this investigation) in compact astrophysical objects have been briefly discussed.

scholarly journals Modulational Instability of Ion-Acoustic Waves and Associated Envelope Solitons in a Multi-Component Plasma

Gases ◽  
2021 ◽  
Vol 1 (3) ◽  
pp. 148-155
Author(s):  
Subrata Banik ◽  
Nadiya Mehzabeen Heera ◽  
Tasfia Yeashna ◽  
Md. Rakib Hassan ◽  
Rubaiya Khondoker Shikha ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Modulational Instability ◽  
Reductive Perturbation Method ◽  
Ion Temperature ◽  
Ion Acoustic Waves ◽  
Stable Domain ◽  
Laboratory Plasmas ◽  
Electrons And Positrons ◽  
Ion Acoustic ◽  
Component Plasma

A generalized plasma model with inertial warm ions, inertialess iso-thermal electrons, super-thermal electrons and positrons is considered to theoretically investigate the modulational instability (MI) of ion-acoustic waves (IAWs). A standard nonlinear Schrödinger equation is derived by applying the reductive perturbation method. It is observed that the stable domain of the IAWs decreases with ion temperature but increases with electron temperature. It is also found that the stable domain increases by increasing (decreasing) the electron (ion) number density. The present results will be useful in understanding the conditions for MI of IAWs which are relevant to both space and laboratory plasmas.

scholarly journals Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
S. A. El-Wakil ◽  
Essam M. Abulwafa ◽  
E. K. El-Shewy ◽  
H. G. Abdelwahed ◽  
Hamdi M. Abd-El-Hamid
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Algebraic Method ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Relativistic Plasma ◽  
Plasma Parameters ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Weakly Relativistic Plasma

The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width) of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Propagation of ion acoustic waves in a warm multicomponent plasma with an electron beam

1999 ◽  
Vol 61 (2) ◽  
pp. 177-189 ◽  
Author(s):  
W. M. MOSLEM
Keyword(s):  
Electron Beam ◽  
Evolution Equation ◽  
Acoustic Waves ◽  
Reductive Perturbation Method ◽  
Negative Ion ◽  
Ion Acoustic Waves ◽  
Ion Density ◽  
Basic Set ◽  
Ion Acoustic ◽  
Small Wave

The nonlinear wave structures of small-amplitude ion acoustic waves in a warm plasma with adiabatic negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures) in the vicinity of the critical negative-ion density are investigated using reductive perturbation method. The basic set of equations is reduced to an evolution equation that includes quadratic and cubic nonlinearities. The effective potential of this equation agrees exactly, for small wave amplitudes, with the Sagdeev potential obtained from the original fluid equations using a pseudopotential method. This implies that the evolution equation holds not only in the vicinity of the critical negative-ion density but also in the whole range of negative-ion density under the condition of small wave amplitude.

Higher order contributions to ion acoustic solitary waves in a plasma consisting of warm ions and nonisothermal electrons

1982 ◽  
Vol 60 (4) ◽  
pp. 392-396 ◽  
Author(s):  
M. K. Kalita ◽  
S. Bujarbarua
Keyword(s):  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Reductive Perturbation Method ◽  
Electron Velocity ◽  
Nonlinear Propagation ◽  
Third Order ◽  
Ion Acoustic Waves ◽  
Electron Velocity Distribution ◽  
The Third ◽  
Ion Acoustic

Considering the electron velocity distribution far from Maxwellian, we have investigated the nonlinear propagation of ion acoustic waves in a plasma consisting of warm ions. The solitary wave solution has been obtained for this case retaining terms up to the third order in the usual reductive perturbation method.

scholarly journals Two-Dimensional Nonlinear Propagation of Ion Acoustic Waves through KPB and KP Equations in Weakly Relativistic Plasmas

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
M. G. Hafez ◽  
M. R. Talukder ◽  
M. Hossain Ali
Keyword(s):  
Acoustic Waves ◽  
Finite Amplitude ◽  
Reductive Perturbation Method ◽  
Nonlinear Propagation ◽  
Two Dimensional ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Component Plasma ◽  
Basic Characteristics ◽  
Superthermal Electrons And Positrons

Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.

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