Shock wave occurrence and soliton propagation in polariton condensates

2017 ◽  
Vol 95 (12) ◽  
pp. 1234-1238 ◽  
Author(s):  
A.M. Belounis ◽  
S. Kessal
Keyword(s):  
Shock Wave ◽  
Burgers Equation ◽  
Vries Equation ◽  
Reductive Perturbation Method ◽  
Pitaevskii Equation ◽  
Soliton Propagation ◽  
Modified Burgers Equation ◽  
Reductive Perturbation ◽  
De Vries ◽  
Dispersionless Limit

We study the effects of the gain and the loss of polaritons on the wave propagation in polariton condensates. This system is described by a modified Gross–Pitaevskii equation. In the case of small damping, we use the reductive perturbation method to transform this equation; we get a modified Burgers equation in the dispersionless limit and a damped Korteweg – de Vries equation in a more general case. We demonstrate that the shock wave occurrence depends on the gain and the loss of polaritons in the dispersionless polariton condensate. The resolution of the damped Korteweg – de Vries equation shows that the soliton behaves like a damped wave in the case of a constant damping. Based on an asymptotic solution, the survival time and the distance traveled by this soliton are evaluated. We solve the damped Korteweg – de Vries equation and the modified Gross–Pitaevskii numerically to validate the analytical calculations and discuss especially the soliton propagation in the system.

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 Ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 563-567 ◽  
Author(s):  
Jianyong Wang ◽  
Ying Zeng ◽  
Zufeng Liang ◽  
Yani Xu ◽  
Yuanxiang Zhang
Keyword(s):  
Acoustic Waves ◽  
Vries Equation ◽  
Reductive Perturbation Method ◽  
Superthermal Electrons ◽  
Ion Plasma ◽  
Electron Positron ◽  
Electrons And Positrons ◽  
Ion Acoustic ◽  
De Vries ◽  
Superthermal Electrons And Positrons

Abstract In this work, we are concerned with the ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons. By using the reductive perturbation method, the Korteweg-de Vries equation is derived from the governing equations of ion acoustic waves. An interesting soliton-cnoidal wave solution of the Korteweg-de Vries equation and its quasi-soliton behaviour are presented. The influence of electron superthermality, positron superthermality and positron concentration ratio on characteristics of the quasi-soliton is confirmed to be significant.

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

Solition Wave of Car-Following Model with Anticipation Effect

2015 ◽  
Vol 738-739 ◽  
pp. 504-507
Author(s):  
Ji Qun Wu ◽  
Shuang Ke Li
Keyword(s):  
Burgers Equation ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Nonlinear Characteristics ◽  
Car Following ◽  
De Vries ◽  
Car Following Model ◽  
Anticipation Effect ◽  
Solition Wave

In this paper, the nonlinear analysis is conducted for the car-following model with the consideration of the anticipation effect in single line, which was proposed by Peng guanghan. We study the nonlinear characteristics of the model by applying the reductive perturbation method, and drive the Burgers equation, the Korteweg-de-Vries (KDV) equation and the modified Korteweg-de-Vries (MKDV) equation respectively. We find that the above nonlinear equations for this model are identical with those equations for the Full velocity difference model.

The shock wave solutions of modified ZK Burgers equation in inhomogeneous dusty plasmas

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Liping Zhang ◽  
Jiangqiong Zheng ◽  
Chenxiao Liu ◽  
Jun Ma
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
External Magnetic Field ◽  
Wave Solution ◽  
Burgers Equation ◽  
Dusty Plasmas ◽  
Travelling Wave ◽  
Reductive Perturbation Method ◽  
Wave Transformation ◽  
Shock Wave Solution

Abstract This paper offers a shock wave solution to modified Zakharov–Kuznetsov (MZK) Burgers equation in inhomogeneous dusty plasmas with external magnetic field. For this purpose, the fluid equations are reduced to an MZK Burgers equation containing variable coefficients by reductive perturbation method. With the aid of travelling-wave transformation technique, we obtain the analytical oscillatory shock wave solution and monotonic shock wave solution for MZK Burgers equation. The effects of inhomogeneity, external magnetic field, dust charge variation on characteristics of two types of shock waves are examined in detail.

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