Higher order nonlinear and dispersive effects on ion-acoustic solitary waves

1991 ◽  
Vol 69 (7) ◽  
pp. 822-827 ◽  
Author(s):  
K. P. Das ◽  
S. R. Majumdar
Keyword(s):  
Solitary Wave ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Inhomogeneous Equation ◽  
Governing Equations ◽  
First Order ◽  
Ion Acoustic Solitary Waves ◽  
Reductive Perturbation ◽  
Ion Acoustic ◽  
Higher Order Corrections

Starting from an integrated form of the system of governing equations in terms of pseudopotential, higher order nonlinear and dispersive effects are obtained for an ion-acoustic solitary wave. The advantage of the method developed here is that instead of solving a second-order inhomogeneous differential equation at each order in the reductive perturbation method, we are to solve a first-order inhomogeneous equation at each order. Expressions are obtained for both the Mach number and the width of the solitary wave as functions of amplitude, including higher order corrections.

Effects of higher order contribution and of ion temperature on ion-acoustic solitary waves

1979 ◽  
Vol 57 (3) ◽  
pp. 490-495 ◽  
Author(s):  
C. S. Lai
Keyword(s):  
Solitary Waves ◽  
Stationary Solutions ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Inhomogeneous Equation ◽  
Ion Temperature ◽  
Coupled Equations ◽  
Basic Set ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

The combined effects of ion temperature and higher order corrections on ion-acoustic solitary waves are studied on the basis of the reductive perturbation method. The basic set of fluid equations for warm-ion fluid are reduced to the renormalized warm-ion Korteweg – de Vries equation for the first-order perturbed potential and a renormalized linear inhomogeneous equation for the second-order perturbed potential. Stationary solutions of the coupled equations are obtained, and the velocity and width of solitons calculated are in agreement with the experimental observation.

Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons

2009 ◽  
Vol 75 (5) ◽  
pp. 593-607 ◽  
Author(s):  
SK. ANARUL ISLAM ◽  
A. BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Perturbation Expansion ◽  
Magnetized Plasma ◽  
Wave Number ◽  
First Order ◽  
Zk Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

AbstractA theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.

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

1990 ◽  
Vol 44 (2) ◽  
pp. 253-263 ◽  
Author(s):  
A. Roy Chowdhury ◽  
Gobinda Pakira ◽  
S. N. Paul ◽  
K. Roy Chowdhury
Keyword(s):  
Perturbation Theory ◽  
Solitary Wave ◽  
Nonlinear Waves ◽  
Critical Analysis ◽  
Higher Order ◽  
Relativistic Plasma ◽  
Reductive Perturbation ◽  
Two Temperatures ◽  
Higher Order Corrections ◽  
Two Temperature

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 bl, and bn characterising the non-isothermal nature are depicted graphically and com-pared with previous results.

Contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic warm plasma. Part 2. Non-isothermal case

1995 ◽  
Vol 53 (2) ◽  
pp. 245-252 ◽  
Author(s):  
S. K. El-Labany ◽  
S. M. Shaaban
Keyword(s):  
Perturbation Theory ◽  
Acoustic Waves ◽  
Higher Order ◽  
Inhomogeneous Equation ◽  
Ion Acoustic Waves ◽  
Coupled Equations ◽  
Reductive Perturbation ◽  
Ion Acoustic ◽  
Renormalization Method ◽  
Linear Inhomogeneous Equation

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of a warm ion fluid and hot non- isothermal electrons is studied using reductive perturbation theory. At the lowest order of the perturbation theory a modified Korteweg–de Vries equation is obtained. At the next order a linear inhomogeneous equation is obtained. The stationary solution of the coupled equations is obtained using the renormalization method introduced by Kodama and Taniuti for reductive perturbation theory.

Nonlinear Evolution of External Ideal MHD Modes Near the Boundary of Marginal Stability

1984 ◽  
Vol 39 (3) ◽  
pp. 288-308
Author(s):  
E. Rebhan
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Evolution ◽  
Nonlinear Boundary Conditions ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Marginal Stability ◽  
Amplitude Equations ◽  
Full Generality ◽  
Ideal Mhd ◽  
Higher Order Corrections

AbstractThe nonlinear evolution of external ideal MHD-modes is determined from the equations of ideal MHD by employing a reductive perturbation method which uses a driving parameter for expansion. The reduction of the plasma equations is the same as for internal modes and was treated previously [1]. A main problem arising in addition for external modes is the reduction of the nonlinear boundary conditions. The set of reduced boundary conditions is obtained on the undisplaced boundary in the marginally stable equilibrium position. Another additional problem arises from the fact that the linear MHD operator is only selfadjoint for linear eigenmodes but not for the higher order mode corrections. This complicates the determination of nonlinear amplitude equations for the marginal mode which are obtained from solubility conditions. The amplitude equations are qualitatively the same as for internal modes. Quantitatively, the calculation of the coefficients in these is different. Explicit expressions for the coefficients are derived in full generality. The effect of higher order corrections to the nonlinear amplitude equations is discussed quantitatively for one of two possible cases and qualitatively for the other.

scholarly journals Propagation of ion-acoustic solitary waves in a relativistic electron-positron-ion plasma

2011 ◽  
Vol 89 (3) ◽  
pp. 299-309 ◽  
Author(s):  
E. Saberian ◽  
A. Esfandyari-Kalejahi ◽  
M. Akbari-Moghanjoughi
Keyword(s):  
Solitary Wave ◽  
Relativistic Electron ◽  
Solitary Waves ◽  
Thermal Energy ◽  
Large Amplitude ◽  
Considerable Effect ◽  
Potential Well ◽  
Electron Positron ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

The propagation of large amplitude ion-acoustic solitary waves (IASWs) in a fully relativistic plasma consisting of cold ions and ultra-relativistic hot electrons and positrons is investigated using the Sagdeev pseudopotential method in a relativistic hydrodynamics model. The effects of streaming speed of the plasma fluid, thermal energy, positron density, and positron temperature on large amplitude IASWs are studied by analysis of the pseudopotential structure. It is found that in regions in which the streaming speed of the plasma fluid is larger than that of the solitary wave, by increasing the streaming speed of the plasma fluid, the depth and width of the potential well increase, resulting in narrower solitons with larger amplitude. This behavior is opposite to the case where the streaming speed of the plasma fluid is less than that of the solitary wave. On the other hand, an increase in the thermal energy results in wider solitons with smaller amplitude, because the depth and width of the potential well decrease in that case. Additionally, the maximum soliton amplitude increases and the width becomes narrower as a result of an increase in positron density. It is shown that varying the positron temperature does not have a considerable effect on the width and amplitude of IASWs. The existence of stationary soliton-like arbitary amplitude waves is also predicted in fully relativistic electron-positron-ion (EPI) plasmas. The effects of streaming speed of the plasma fluid, thermal energy, positron density, and positron temperature on these kinds of solitons are the same for large amplitude IASWs.

Effect of the third-order contribution on ion-acoustic solitary waves

1979 ◽  
Vol 57 (12) ◽  
pp. 2136-2142 ◽  
Author(s):  
C. S. Lai
Keyword(s):  
Solitary Waves ◽  
Order Approximation ◽  
Reductive Perturbation Method ◽  
Renormalization Scheme ◽  
Third Order ◽  
The Third ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
Third Order Approximation ◽  
Secular Terms

The effect of the third-order corrections on ion-acoustic solitary waves is studied on the basis of the reductive perturbation method. The secular terms in the third-order approximation are eliminated by employing the renormalization scheme of Kodama and Taniuti in an unambiguous manner. It is found that the contribution of the third-order corrections to the soliton velocities and widths is rather minimal.

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