Soliton molecules, nonlocal symmetry and CRE method of the KdV equation with higher-order corrections

2020 ◽  
Vol 95 (7) ◽  
pp. 075202
Author(s):  
Bo Ren ◽  
Ji Lin
Keyword(s):  
Kdv Equation ◽  
Higher Order ◽  
Nonlocal Symmetry ◽  
The Kdv Equation ◽  
Higher Order Corrections

Higher-order corrections to the ion-acoustic waves in a relativistic plasma (isothermal case)

1988 ◽  
Vol 40 (2) ◽  
pp. 359-367 ◽  
Author(s):  
Gobinda Pada Pakira ◽  
A. Roy Chowdhury ◽  
S. N. Paul
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Perturbation Technique ◽  
Type Equation ◽  
Higher Order ◽  
Relativistic Plasma ◽  
Singular Perturbation Technique ◽  
Ion Acoustic ◽  
Physical Profile ◽  
Higher Order Corrections

As a continuation of our earlier work, we have analysed the higher-order perturbative corrections to the formation of (ion-acoustic) solitary waves in a relativistic plasma. It is found that the relativistic considerations affect the amplitude and width variation - as conjectured in our previous paper. Our analysis employs a higher-order singular perturbation technique, with the elimination of secular terms in stages. In this way we arrive at an inhomogeneous KdV-type equation, which is then solved exactly. At this point a new phenomena arises at a critical value of the phase velocity at which the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched co-ordinate is then used to derive a modified KdV equation. In both cases we have numerically computed the specific physical profile of the new solitary wave and its width.

Effect of Higher-Order Corrections on the Propagation of Nonlinear Dust-Acoustic Solitary Waves in Mesospheric Dusty Plasmas

2006 ◽  
Vol 61 (7-8) ◽  
pp. 316-322 ◽  
Author(s):  
Sayed A. Elwakil ◽  
Mohamed T. Attia ◽  
Mohsen A. Zahran ◽  
Emad K. El-Shewy ◽  
Hesham G. Abdelwahed
Keyword(s):  
Acoustic Waves ◽  
Kdv Equation ◽  
Type Equation ◽  
Dusty Plasmas ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Dust Acoustic Solitary Waves ◽  
Dust Acoustic ◽  
Renormalization Method ◽  
Higher Order Corrections

The contribution of the higher-order correction to nonlinear dust-acoustic waves are studied using the reductive perturbation method in an unmagnetized collisionless mesospheric dusty plasma. A Korteweg - de Vries (KdV) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation, and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution is achived via renormalization method

The Effect of Higher-Order Corrections on the Propagation of Nonlinear Dust-Acoustic Solitary Waves in a Dusty Plasma with Nonthermal Ions Distribution

2008 ◽  
Vol 63 (5-6) ◽  
pp. 261-272 ◽  
Author(s):  
Hesham G. Abdelwahed ◽  
Emad K. El-Shewy ◽  
Mohsen A. Zahran ◽  
Mohamed T. Attia
Keyword(s):  
Dusty Plasma ◽  
Kdv Equation ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Charged Dust ◽  
Ion Distributions ◽  
Kdv Equations ◽  
Dust Acoustic ◽  
Renormalization Method ◽  
Higher Order Corrections

Propagation of nonlinear dust-acoustic (DA) waves in a unmagnetized collisionless mesospheric dusty plasma containing positively and negatively charged dust grains and nonthermal ion distributions are investigated. For nonlinear DA waves, a reductive perturbation method is employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential. As it is well-known, KdV equations contain the lowest-order nonlinearity and dispersion, and consequently can be adopted for only small amplitudes. As the wave amplitude increases, the width and velocity of a soliton can not be described within the framework of KdV equations. So, we extend our analysis and take higher-order nonlinear and dispersion terms into account to clarify the essential effects of higher-order corrections. Moreover, in order to study the effects of higher-order nonlinearity and dispersion on the output solution, we address an appropriate technique, namely the renormalization method.

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