An analysis of higher order terms for ion-acoustic waves by use of the modified Poincaré-Lighthill-Kuo method

AbstractThe propagation of dust ion acoustic waves (DIAWs) in a weakly inhomogeneous, weakly coupled, collisionless, and unmagnetized four components dusty plasma are examined. The fluid system considered in this work consists of cold positive ions, cold negatively and positively charged dust particles associated with isothermal electrons. For nonlinear (DIAW) waves, a reductive perturbation method was employed to obtain the variable coefficients Kortewege-de Vries (KdV) equation for the first-order potential. For local inhomogenity, the present system admits the coexistence of rarefactive and compressive solitons. As a matter of fact, when the wave amplitude enlarged, the width and velocity of the wave deviate from the prediction of the KdV equation. It means that we have to extend our analysis to obtain the variable coefficients Kortewege-de Vries (KdV) equation with fifth-order dispersion term. For locally constant parameters, the higher-order solution for the resulting equation has been achieved via what is called perturbation technique. The effects of positive and negative dust charge fluctuations on the higher-order soliton amplitude and width of electrostatic solitary structures are outlined.

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Contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic warm plasma. Part 1. Isothermal case

Journal of Plasma Physics ◽

10.1017/s0022377800017293 ◽

1993 ◽

Vol 50 (3) ◽

pp. 495-504 ◽

Cited By ~ 24

Author(s):

S. K. El-Labany

Keyword(s):

Perturbation Theory ◽

Acoustic Waves ◽

Type Equation ◽

Higher Order ◽

Ion Acoustic Waves ◽

Ion Acoustic ◽

Warm Plasma ◽

Relativistic Parameter ◽

Renormalization Method ◽

Parameter Dependent

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of warm ion-fluid and hot isothermal electrons is investigated using reductive perturbation theory. A Korteweg-de Vries-type equation, with temperature- and relativistic-parameter-dependent coefficients is obtained. The renormalization method is applied to the equations obtained from the different orders of perturbation theory to obtain a stationary solution. Relativistic cold and non-relativistic warm plasma limits are considered in order to make comparisons with previous results.

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Modulational instability of ion acoustic waves in the presence of density gradients

Canadian Journal of Physics ◽

10.1139/p79-091 ◽

1979 ◽

Vol 57 (5) ◽

pp. 642-644 ◽

Cited By ~ 5

Author(s):

I. R. Durrani ◽

G. Murtaza ◽

H. U. Rahman

Keyword(s):

Density Gradient ◽

Acoustic Waves ◽

Schrodinger Equation ◽

Modulational Instability ◽

Collisionless Plasma ◽

Higher Order ◽

Density Gradients ◽

Ion Acoustic Waves ◽

Ion Acoustic ◽

Non Linear

Using the Krylov–Bogoliubov–Mitropolsky method of perturbation for weak non-linearities, we study the modulational instability of ion-acoustic waves in a collisionless plasma in the presence of a density gradient. We find that the density gradient of second or higher order of perturbation does not effect the dispersion and the non-linearity coefficients in the non-linear Schrödinger equation.

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

Journal of Plasma Physics ◽

10.1017/s0022377800018158 ◽

1995 ◽

Vol 53 (2) ◽

pp. 245-252 ◽

Cited By ~ 29

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.

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