The reductive perturbation method and the Korteweg-de Vries hierarchy

1995 ◽  
Vol 39 (1-3) ◽  
pp. 389-403 ◽  
Author(s):  
R. A. Kraenkel ◽  
J. G. Pereira ◽  
M. A. Manna
Keyword(s):  
Perturbation Method ◽  
Reductive Perturbation Method ◽  
Reductive Perturbation ◽  
De Vries

Effect of higher-order nonlinearity on propagation of nonlinear ion-acoustic waves in a collisionless plasma consisting of negative ions

1986 ◽  
Vol 35 (2) ◽  
pp. 219-237 ◽  
Author(s):  
S. G. Tagare ◽  
R. Virupakshi Reddy
Keyword(s):  
Perturbation Method ◽  
Vries Equation ◽  
Negative Ions ◽  
Higher Order ◽  
Reductive Perturbation Method ◽  
Coupled Equations ◽  
Basic Set ◽  
Reductive Perturbation ◽  
De Vries ◽  
Cold Ions

The combined effects of negative ions and higher-order nonlinearity on ionacoustic solitons are studied using the reductive perturbation method. The basic set of fluid equations for a plasma consisting of negative cold ions, positive cold ions and hot electrons (non-isothermal and isothermal) reduces to the modified Korteweg-de Vries equation and the Korteweg-de Vries equation for the first-order potential, and to the linear inhomogeneous equation for the second-order potential. Stationary solutions of the coupled equations are obtained in the case of negative ions, retaining terms up to the third order in the usual reductive perturbation method.

Localized coherent nonlinear wave structures in dusty plasma with non-thermal ions

2007 ◽  
Vol 73 (6) ◽  
pp. 921-932 ◽  
Author(s):  
TARSEM SINGH GILL ◽  
CHANCHAL BEDI ◽  
NARESHPAL SINGH SAINI ◽  
HARVINDER KAUR
Keyword(s):  
Perturbation Method ◽  
Solitary Waves ◽  
Vries Equation ◽  
Thermal Parameter ◽  
Reductive Perturbation Method ◽  
Double Layers ◽  
Dust Charge ◽  
Dust Acoustic Solitary Waves ◽  
Reductive Perturbation ◽  
Dust Acoustic

AbstractIn the present research paper, the characteristics of dust-acoustic solitary waves (DASWs) and double layers (DLs) are studied. Ions are treated as non-thermal and variable dust charge is considered. The Korteweg–de Vries equation is derived using a reductive perturbation method. It is noticed that compressive solitons are obtained up to a certain range of relative density δ (=ni0/ne0) beyond which rarefactive solitons are observed. The study is further extended to investigate the possibility of DLs. Only compressive DLs are permissible. Both DASWs and DLs are sensitive to variation of the non-thermal parameter.

scholarly journals The Modified Reductive Perturbation Method as Applied to the Boussinesq Equation

2007 ◽  
Vol 62 (7-8) ◽  
pp. 347-352 ◽  
Author(s):  
Hilmi Demiray
Keyword(s):  
Perturbation Method ◽  
Water Waves ◽  
Present Method ◽  
Evolution Equations ◽  
Expansion Method ◽  
Multiple Scale ◽  
Travelling Wave ◽  
Reductive Perturbation Method ◽  
Kdv Hierarchy ◽  
Reductive Perturbation

In this work, we extended the application of “the modified reductive perturbation method” to long water waves and obtained the governing equations of Korteweg - de Vries (KdV) hierarchy. Seeking localized travelling wave solutions to these evolution equations we have determined the scale parameter g1 so as to remove the possible secularities that might occur. To indicate the effectiveness and the elegance of the present method, we studied the problem of the “dressed solitary wave method” and obtained exactly the same result. The present method seems to be fairly simple and practical as compared to the renormalization method and the multiple scale expansion method existing in the current literature

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