Hostname: page-component-54dcc4c588-mz6gc Total loading time: 0 Render date: 2025-09-16T16:09:33.420Z Has data issue: false hasContentIssue false
  • English
  • Français

Application scope of the reductive perturbation method to derive the KdV equation and CKdV equation in dusty plasma

Published online by Cambridge University Press:  17 April 2023

Heng Zhang ,
Yu-Xi Chen Open the ORCID record for Yu-Xi Chen [Opens in a new window] ,
Lin Wei Open the ORCID record for Lin Wei [Opens in a new window] ,
Fang-Ping Wang ,
Wei-Ping Zhang Open the ORCID record for Wei-Ping Zhang [Opens in a new window]  and
Wen-Shan Duan
Heng Zhang*
Affiliation:
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Yu-Xi Chen
Affiliation:
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Lin Wei
Affiliation:
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Fang-Ping Wang
Affiliation:
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Wei-Ping Zhang
Affiliation:
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
Wen-Shan Duan*
Affiliation:
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, PR China
*
†Email addresses for correspondence: zhangheng@nwnu.edu.cn, duanws@nwnu.edu.cn
†Email addresses for correspondence: zhangheng@nwnu.edu.cn, duanws@nwnu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The application scopes of two different reductive perturbation methods to derive the Korteweg–de Vries (KdV) equation and coupled KdV (CKdV) equation in two-temperature-ion dusty plasma are given by using the particle-in-cell (PIC) numerical method in the present paper. It suggests that the reductive perturbation method (RPM) is valid if the amplitude of the CKdV solitary wave is small enough. However, for the KdV solitary wave, RPM is valid not only if the amplitude of the KdV solitary wave is small enough, but also if the nonlinear coefficient of the KdV equation is not tending to zero.

Keywords

dusty plasmasplasma wavesplasma simulation

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 89 , Issue 2 , April 2023 , 905890212
Check for updates
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bandyopadhyay, P., Prasad, G., Sen, A. & Kaw, P.K. 2008 Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma. Phys. Rev. Lett. 101 (6), 065006.CrossRefGoogle Scholar
Barkan, A., Merlino, R.L. & D'Angelo, N. 1995 Laboratory observation of the dust-acoustic wave mode. Phys. Plasmas 2 (10), 3563–3565.CrossRefGoogle Scholar
Couëdel, L., Nosenko, V., Ivlev, A.V., Zhdanov, S.K., Thomas, H.M. & Morfill, G.E. 2010 Direct observation of mode-coupling instability in two-dimensional plasma crystals. Phys. Rev. Lett. 104 (19), 195001.CrossRefGoogle ScholarPubMed
Duan, W.S. & Shi, Y.R. 2003 The effect of dust size distribution for two ion temperature dusty plasmas. Chaos, Solitons Fractals 18 (2), 321–328.CrossRefGoogle Scholar
Duan, W.S., Wang, B.R. & Wei, R.J. 1996 The decay of soliton in small blood artery. J. Phys. Soc. Japan 65 (4), 945–947.CrossRefGoogle Scholar
Dubinov, A.E. & Sazonkin, M.A. 2013 Supernonlinear ion-acoustic waves in a dusty plasma. Phys. Wave Phenomena 21 (2), 118–128.CrossRefGoogle Scholar
El-Labany, S.K., El-Taibany, W.F., Mamun, A.A. & Moslem, W.M. 2004 Dust acoustic solitary waves and double layers in a dusty plasma with two-temperature trapped ions. Phys. Plasmas 11 (3), 926–933.CrossRefGoogle Scholar
Emamuddin, M., Yasmin, S. & Mamun, A.A. 2013 Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons. Phys. Plasmas 20 (4), 043705.CrossRefGoogle Scholar
Fortov, V.E., Ivlev, A.V., Khrapak, S.A., Khrapak, A.G. & Morfill, G.E. 2005 Complex (dusty) plasmas: Current status, open issues, perspectives. Phys. Rep. 421 (1–2), 1–103.CrossRefGoogle Scholar
Gao, D.N., Zhang, H., Zhang, J., Li, Z.Z. & Duan, W.S. 2017 Effect of a damping force on dust acoustic waves simulated by particle-in-cell method. Phys. Plasmas 24 (4), 043703.CrossRefGoogle Scholar
Ghorui, M.K., Chatterjee, P. & Wong, C.S. 2013 Head on collision of dust ion acoustic solitary waves in magnetized quantum dusty plasmas. Astrophys. Space Sci. 343 (2), 639–645.CrossRefGoogle Scholar
Ghorui, M.K., Samanta, U.K., Maji, T.K. & Chatterjee, P. 2014 Head-on collisions of two types of dust-acoustic solitons in a magnetized quantum plasma. Astrophys. Space Sci. 352 (1), 159–169.CrossRefGoogle Scholar
Han, J.F., Gao, D.N., Zhang, H., Wang, X.Y. & Duan, W.S. 2015 Effects of the dust size distribution in one-dimensional quantum dusty plasma. Front. Phys. 10 (5), 105201.CrossRefGoogle Scholar
Huang, G.X., Velarde, M.G. & Makarov, V.A. 2001 Dark solitons and their head-on collisions in Bose–Einstein condensates. Phys. Rev. A 64 (1), 013617.CrossRefGoogle Scholar
Kalman, G., Rosenberg, M. & DeWitt, H.E. 2000 Collective modes in strongly correlated Yukawa liquids: waves in dusty plasmas. Phys. Rev. Lett. 84 (26), 6030.CrossRefGoogle ScholarPubMed
Korteweg, D.J. & De Vries, G. 1895 On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Lond. Edinb. Dublin Philos. Mag. J. Sci. 39 (240), 422–443.CrossRefGoogle Scholar
Kumar Tiwari, S. & Sen, A. 2016 Wakes and precursor soliton excitations by a moving charged object in a plasma. Phys. Plasmas 23 (2), 022301.CrossRefGoogle Scholar
Lee, N.C. 2012 Derivation of nonlinear Schrödinger equation for electrostatic and electromagnetic waves in fully relativistic two-fluid plasmas by the reductive perturbation method. Phys. Plasmas 19 (8), 082303.CrossRefGoogle Scholar
Lin, M.M. & Duan, W.S. 2005 The Kadomtsev–Petviashvili (KP), MKP, and coupled KP equations for two-ion-temperature dusty plasmas. Chaos, Solitons Fractals 23 (3), 929–937.CrossRefGoogle Scholar
Merlino, R.L. 2014 25 years of dust acoustic waves. J. Plasma Phys. 80 (6), 773–786.CrossRefGoogle Scholar
Merlino, R.L., Barkan, A., Thompson, C. & D'Angelo, N. 1998 Laboratory studies of waves and instabilities in dusty plasmas. Phys. Plasmas 5 (5), 1607–1614.CrossRefGoogle Scholar
Olivier, C.P., Verheest, F. & Maharaj, S.K. 2016 A small-amplitude study of solitons near critical plasma compositions. J. Plasma Phys. 82 (6), 905820605.CrossRefGoogle Scholar
Ono, H. 1991 Deformation of nonlinear gravity waves due to depth variation. J. Phys. Soc. Japan 60 (12), 4127–4132.CrossRefGoogle Scholar
Pieper, J.B. & Goree, J. 1996 Dispersion of plasma dust acoustic waves in the strong-coupling regime. Phys. Rev. Lett. 77 (15), 3137.CrossRefGoogle ScholarPubMed
Praburam, G. & Goree, J. 1996 Experimental observation of very low-frequency macroscopic modes in a dusty plasma. Phys. Plasmas 3 (4), 1212–1219.CrossRefGoogle Scholar
Qi, X., Xu, Y.X., Duan, W.S. & Yang, L. 2014 The application scope of the reductive perturbation method and the upper limit of the dust acoustic solitary waves in a dusty plasma. Phys. Plasmas 21 (1), 013702.CrossRefGoogle Scholar
Rao, N.N., Shukla, P.K. & Yu, M.Y. 1990 Dust-acoustic waves in dusty plasmas. Planet. Space Sci. 38 (4), 543–546.CrossRefGoogle Scholar
Seadawy, A.R. 2015 Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma. Physica A 439, 124–131.CrossRefGoogle Scholar
Shukla, P.K. 1992 Low-frequency modes in dusty plasmas. Phys. Scr. 45 (5), 504–507.CrossRefGoogle Scholar
Shukla, P.K. 2001 A survey of dusty plasma physics. Phys. Plasmas 8 (5), 1791–1803.CrossRefGoogle Scholar
Shukla, P.K. & Eliasson, B. 2009 Colloquium: fundamentals of dust-plasma interactions. Rev. Mod. Phys. 81 (1), 25.CrossRefGoogle Scholar
Teng, L.W., Chang, M.C., Tseng, Y.P. & Lin, I. 2009 Wave-particle dynamics of wave breaking in the self-excited dust acoustic wave. Phys. Rev. Lett. 103 (24), 245005.CrossRefGoogle ScholarPubMed
Verheest, F. & Hereman, W.A. 2019 Collisions of acoustic solitons and their electric fields in plasmas at critical compositions. J. Plasma Phys. 85 (1), 905850106.CrossRefGoogle Scholar
Wadati, M. 1990 Deformation of solitons in random media. J. Phys. Soc. Japan 59 (12), 4201–4203.CrossRefGoogle Scholar
Wang, D.Z. & Wu, H.T. 2002 Analysis of dusty plasma in the positive column of glow discharges. Chin. Phys. 11 (8), 0799.Google Scholar
Wang, F.P., Han, J.F., Zhang, J., Gao, D.N., Li, Z.Z., Duan, W.S. & Zhang, H. 2018 Numerical simulation of dark envelope soliton in plasma. Phys. Plasmas 25 (3), 032121.CrossRefGoogle Scholar
Washimi, H. & Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17 (19), 996.CrossRefGoogle Scholar
Xie, B.S. & He, K.F. 2001 Nonlinear localized structure in dusty plasma. Chin. Phys. 10 (3), 0214.Google Scholar
Zabusky, N.J. & Kruskal, M.D. 1965 Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (6), 240.CrossRefGoogle Scholar
Zhang, H., Qi, X., Duan, W.S. & Yang, L. 2015 Envelope solitary waves exist and collide head-on without phase shift in a dusty plasma. Sci. Rep. 5 (1), 14239.CrossRefGoogle Scholar
Zhang, H., Yang, Y., Hong, X.R., Qi, X., Duan, W.S. & Yang, L. 2017 Freak oscillation in a dusty plasma. Phys. Rev. E 95 (5), 053207.CrossRefGoogle Scholar
Zhang, J., Yang, Y., Xu, Y.X., Yang, L., Qi, X. & Duan, W.S. 2014 The study of the Poincare–Lighthill–Kuo method by using the particle-in-cell simulation method in a dusty plasma. Phys. Plasmas 21 (10), 103706.CrossRefGoogle Scholar