Higher‐order solution of an ion‐acoustic solitary wave in a plasma

1993 ◽  
Vol 5 (2) ◽  
pp. 409-414 ◽  
Author(s):  
S. Watanabe ◽  
B. Jiang
Keyword(s):  
Solitary Wave ◽  
Higher Order ◽  
Order Solution ◽  
Ion Acoustic

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.

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 Solution of Nonlinear Waves. II. Shock Wave Described by Burgers Equation

1997 ◽  
Vol 66 (4) ◽  
pp. 984-987 ◽  
Author(s):  
Shinsuke Watanabe ◽  
Shingo Ishiwata ◽  
Katsuyuki Kawamura ◽  
Heung Geun Oh
Keyword(s):  
Shock Wave ◽  
Nonlinear Waves ◽  
Burgers Equation ◽  
Higher Order ◽  
Order Solution
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