The evolution of multidimensional shock structures in magnetized dusty plasmas with arbitrary dust size distribution

Original Paper


A theoretical investigation on the evolution of multidimensional nonlinear shock structures has been carried out in magnetized dusty plasmas with nonadiabatic charge fluctuation and arbitrary dust size distribution in present work. A Korteweg–de Vries (KdV) Burgers equation for the multidimensional shock structures is obtained by Reductive Perturbation Method, and the effects of arbitrary dust size distribution, nonadiabatic charge fluctuation and external magnetic field on the multidimensional shock structures’ evolution are illustrated. The results show that there are two types of shock structures, namely, oscillatory shock structures and monotone shock structures. Furthermore, the boundary condition between oscillatory shock structures and monotone shock structures is discussed in great detail.


Nonlinear multidimensional shock structures Magnetized dusty plasmas Charge fluctuation Dust size distribution 





This project is supported by the National Natural Foundation of China under Grant No. 10975114 and Research Projects of Higher Education of Gansu Province under Grant No. 2017A-016.


  1. [1]
    P K Shukla and V P Silin Phys. Scr. 45 508 (1992)ADSCrossRefGoogle Scholar
  2. [2]
    N N Rao, P K Shukla and M Y Yu Planet. Space Sci. 38 543 (1990)ADSCrossRefGoogle Scholar
  3. [3]
    A Barkan, R Merlino and N D Angelo Phys. Plasmas 2 3563 (1995)ADSCrossRefGoogle Scholar
  4. [4]
    Y Nakamura, H Bailung and P K Shukla Phys. Rev. Lett. 83 1602 (1999)ADSCrossRefGoogle Scholar
  5. [5]
    R K Varma, P K Shukla and V Krishan Phys. Rev. E 47 3612 (1993)ADSCrossRefGoogle Scholar
  6. [6]
    J K Xue China. Phys. 12 538 (2003)ADSCrossRefGoogle Scholar
  7. [7]
    M R Jana, A Sen and P K Kaw Phys. Rev. E 48 3930 (1993)ADSCrossRefGoogle Scholar
  8. [8]
    S K El China. Phys. 12 759 (2003)ADSCrossRefGoogle Scholar
  9. [9]
    S A Khrapak and G Morfill Phys. Plasmas 8 2629 (2001)ADSCrossRefGoogle Scholar
  10. [10]
    M R Gupta, S Sarkar, S Ghosh, M Debnath and M Khan Phys. Rev. E 63 467 (2001)CrossRefGoogle Scholar
  11. [11]
    B S Xie Chin. Phys. 9 922 (2000)CrossRefGoogle Scholar
  12. [12]
    S Ghosh, T K Chaudhuri, S Sarkar, K Manoranjan and M R Gupta Phys. Rev. E 65 106 (2002)Google Scholar
  13. [13]
    Y L Wang, X Y Guo, Y Z Lu, and X D Wang Phys. Lett. A 380 215–221 (2015)ADSCrossRefGoogle Scholar
  14. [14]
    M Bacha and M Tribeche Phys. Plasmas 23 083702 (2016)ADSCrossRefGoogle Scholar
  15. [15]
    H Alinejad and M Shahmansory Phys. Plasmas 19 083705 (2012)ADSCrossRefGoogle Scholar
  16. [16]
    M G Shah, M M Rahman, M R Hossen, A A Mamun Plasma Physics Reports 42 168 (2016)ADSCrossRefGoogle Scholar
  17. [17]
    Y R Ma, C L Wang, J R Zhang, J A Sun, W S Duan and L Yang Phys. Plasmas 19 113702 (2012)ADSCrossRefGoogle Scholar
  18. [18]
    H Zhang, X Y Wang, W S Duan and L Yang Indian J. Phys. 90 1207 (2016)ADSCrossRefGoogle Scholar
  19. [19]
    G Banerjee and S Maitra Phys. Plasmas 22 043708 (2015)ADSCrossRefGoogle Scholar
  20. [20]
    J R Asbridge, S J Bame and I B Strong J. Geophys. Res. 73 5777 (1968)ADSCrossRefGoogle Scholar
  21. [21]
    R A Cairns, A A Mamun, R O Dendy, R Bostrom and P K Shukla Geophys. Res. Lett. 22 2709 (1995)ADSCrossRefGoogle Scholar
  22. [22]
    J E Allen Phys. Scr. 45 497 (1992)ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    S Ghosh, R Bharuthram, M Khan and M R Gupta Phys. Plasmas 11 3602 (2004)ADSCrossRefGoogle Scholar
  24. [24]
    H Washimi and T Taniuti Phys. Rev. Lett. 17 996 (1966)ADSCrossRefGoogle Scholar
  25. [25]
    S V Singh and N N Rao J. Plasma Phys. 60 541 (1998)ADSCrossRefGoogle Scholar
  26. [26]
    P Meuris Planet Space Sci. 45 1171 (1997)ADSCrossRefGoogle Scholar
  27. [27]
    G J He and W S Duan Phys. Plasmas 15 043702 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  1. 1.School of SciencesLanZhou University of TechnologyLanzhouChina

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