, 91:88 | Cite as

Nonlinear propagation of ion plasma waves in dust-ion plasma including quantum-relativistic effect

  • H SahooEmail author
  • K K Mondal
  • B Ghosh


In this paper we have theoretically investigated the quantum and relativistic effects on ion plasma wave in an unmagnetised dust-ion plasma. By using the method of normal mode analysis, we have obtained a linear dispersion relation. It has been analysed numerically for quantum and relativistic effects on the propagation of ion plasma wave. By using the standard reductive perturbation technique, we have derived a Korteweg–de Vries (KdV) equation which describes the nonlinear propagation of the wave. Numerically, it is shown that only compressive type of soliton can exist in the plasma under consideration. It is found that the solitary wave profile depends significantly on the quantum and relativistic parameters. The dust size, dust charge and the dust number density are also shown to have significant influences on these solitary waves. The results of this present investigation have some relevance to the nonlinear propagation of ion plasma wave in some astrophysical, space and laboratory plasma environments.


Relativistic effect quantum plasma ion plasma wave ion streaming 


52.27.Ny 52.27.Lw 52.20.−j 52.35 Fp 



The authors thank the anonymous reviewer for some useful suggestions which have helped to improve the presentation of the paper.


  1. 1.
    G Manfredi, Fields Inst. Commun. 46, 263 (2005)Google Scholar
  2. 2.
    C Grabbe, J. Geophys. Res. 94, 17299 (1989)ADSCrossRefGoogle Scholar
  3. 3.
    M Opher, L O Silva, D E Dauger, V K Decyk and J M Dawson, Phys. Plasmas 8, 2454 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    H Ikezi, Phys. Fluids 16, 1668 (1973)ADSCrossRefGoogle Scholar
  5. 5.
    M Marklund and P K Shukla, Rev. Mod. Phys. 78, 591 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    S H Glenzer and R Redmer, Rev. Mod. Phys. 81, 1625 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    P A Markowich, C A Ringhofer and C Schmeiser, Semiconductor equations (Springer, Vienna, New York, 1990)CrossRefGoogle Scholar
  8. 8.
    P K Shukla and B Eliasson, Phys. Rev. Lett. 96, 245001 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    P K Shukla and B Eliasson, Phys. Rev. Lett. 99, 096401 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    H Sahoo, B Ghosh and K K Mondal, The African Rev. Phys. 11, 0035 (2016)Google Scholar
  11. 11.
    B Ghosh and K P Das, J. Plasma Phys. 40(3), 545 (1988)ADSCrossRefGoogle Scholar
  12. 12.
    Shalini and N S Saini, J. Plasma Phys. 81, 905810316 (2015)Google Scholar
  13. 13.
    N N Rao, P K Shukla and M Y Yu, Planet. Space Sci. 38, 543 (1990)ADSCrossRefGoogle Scholar
  14. 14.
    R Z Sagdeev, Reviews of plasma physics edited by M A Leontovich (Consultants Bureau, New York, 1966) Vol. 4, pp. 23–91Google Scholar
  15. 15.
    N Y Kotsarenko et al, Planet Space Sci. 46, 429 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    A Barkan, R L Merlino and N D Angelo, Phys. Plasmas 2, 3563 (1995)ADSCrossRefGoogle Scholar
  17. 17.
    G C Das and S N Paul, Phys. Fluids 28, 823 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    Y Nejoh, J. Plasma Phys. 38, 439 (1987)ADSCrossRefGoogle Scholar
  19. 19.
    H H Kuehl and G Y Zhang, Phys. Fluids B  3, 26 (1991)ADSCrossRefGoogle Scholar
  20. 20.
    A Roychowdhury, G Pakira and S N Paul, IEEE Trans. Plasma Sci. 26, 987 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    T S Gill, A S Bains and N S Saini, Can. J. Phys. 87, 861 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    B C Kalita, R Das and H K Sarmah, Phys. Plasmas 18, 012304 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    H Pakzad, Astrophys. Space Sci. 332, 269 (2011).ADSCrossRefGoogle Scholar
  24. 24.
    T S Gill, A Singh, H Kaur, N S Saini and P Bala, Phys. Lett. A 361, 364 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    M Opher, L O Silva, D E Dauger, V K Decyk and J M Dawson, Phys. Plasmas 8, 2544 (2001)CrossRefGoogle Scholar
  26. 26.
    Y D Jung, Phys. Plasmas 8, 3842 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    S Ali and P K Shukla, Phys. Plasmas 13, 022313 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    B Sahu, Pramana – J. Phys. 76, 933 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    T S Gill, A S Bains and C Bedi, J. Phys. Conf. Ser. 208, 012040 (2010)CrossRefGoogle Scholar
  30. 30.
    B Ghosh, S Chandra and S N Paul, Pramana – J. Phys. 78(5), 779 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    T Esirkepov, M Borghesi, S V Bulanov, G Mourou and T Tajima, Phys. Rev. Lett. 92, 175003-1 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    F Melia and H Falcke, Ann. Rev. Astron. Astrophys. 39, 309 (2001)ADSCrossRefGoogle Scholar
  33. 33.
    M E Dieckmann, Nonlinear Process. Geophys. 15, 831 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    S L Shapiro and S.A Teukolsky, Black holes, white dwarfs and neutron stars: The physics of compact objects (Wiley-VCH, Verlag, Weinhelm, 2004)Google Scholar
  35. 35.
    N S Saini and K Singh, Phys. Plasmas 23, 103701 (2016)ADSCrossRefGoogle Scholar
  36. 36.
    J E Gunn and J P Ostriker, Astrophys. J. 165, 523 (1971)ADSCrossRefGoogle Scholar
  37. 37.
    L Stenflo and N L Tsintsadze, Astrophys. Space Sci. 64, 513 (1979)ADSCrossRefGoogle Scholar
  38. 38.
    L Stenflo and P K Shukla, IEEE Trans. Plasma Sci. 29, 208 (2001)ADSCrossRefGoogle Scholar
  39. 39.
    F Haas, L G Garcia, J Goedert and G Manfredi, Phys. Plasmas 10, 3858 (2003)ADSCrossRefGoogle Scholar
  40. 40.
    G Manfredi and F Haas, Phys. Rev. B 64, 075316 (2001)ADSCrossRefGoogle Scholar
  41. 41.
    C L Gardner and C Ringhofer, Phys. Rev. E 53, 157 (1996)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of PhysicsJadavpur UniversityKolkataIndia
  2. 2.Sovarani Memorial College, JagatballavpurHowrahIndia

Personalised recommendations