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Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma

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Abstract

In this paper, we propose a computational method for nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. Many types of solitary waves including soliton solutions, N-soliton solutions and singular N-soliton solutions are derived. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Furthermore, the effects of inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed.

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References

  1. S. Ali, W.M. Moslem, P.K. Shukla, R. Schlickeiserd, Phys. Plasmas 14, 082307-1 (2007)

    Article  ADS  Google Scholar 

  2. U.M. Abdelsalam, W.M. Moslem, S. Ali, P.K. Shukla, Phys. Lett. A 372, 4923 (2008)

    Article  ADS  MATH  Google Scholar 

  3. Y.D. Jung, Phys. Plasmas 8, 3842 (2001)

    Article  ADS  Google Scholar 

  4. S.A. Khan, W. Masood, Phys. Plasmas 15, 062301-1 (2008)

    ADS  Google Scholar 

  5. S.A. Khan, Q. Haque, Chin. Phys. Lett. 25, 4329 (2008)

    Article  ADS  Google Scholar 

  6. I. Kourakis, W.M. Moslem, U.M. Abdelsalam, R. Sabry, P.K. Shukla, Plasma Fusion Res. 4, 1 (2009)

    Article  Google Scholar 

  7. W.M. Moslem, S. Ali, P.K. Shukla, X.Y. Tang, G. Rowlands, Phys. Plasmas 14, 082308-1 (2007)

    ADS  Google Scholar 

  8. R. Sabry, W.M. Moslem, P.K. Shukla, Phys. Lett. A 372, 5691 (2008)

    Article  ADS  MATH  Google Scholar 

  9. H. Washimi, T. Taniuti, Phys. Rev. Lett. 17, 996 (1966)

    Article  ADS  Google Scholar 

  10. Y.Y. Wang, J.F. Zhang, Phys. Lett. A 372, 6509 (2008)

    Article  ADS  MATH  Google Scholar 

  11. W. Hereman, A. Nuseir, Math. Comput. Simul. 43, 13 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in 13th World Congress on Computation and Applied Mathematics (Criterion Press, Dublin, 1991), Vol. 2, p. 842

  13. W. Hereman, W. Zhuang, Symbolic computation of solitons with Macsyma, in Computation and Applied Mathematics II: Differential Equations, edited by W.F. Ames, P.J. Van der Houwen (North Holland, Amsterdam, 1992), pp. 287–296

  14. R. Hirota, Phys. Rev. Lett. 27, 1192 (1971)

    Article  ADS  MATH  Google Scholar 

  15. R. Hirota, The direct method in soliton theory (Cambridge University Press, Cambridge, 2004)

  16. R. Hirota, J. Phys. Soc. Jpn 33, 1459 (1972)

    Article  ADS  Google Scholar 

  17. R. Hirota, J. Math. Phys. 14, 805 (1973)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. A. Bandyopadhyoy, K.P. Das, J. Plasma Phys. 62, 255 (1999)

    Article  ADS  Google Scholar 

  19. L. Ying, G. Yi-Tian, S. Zhi-Yuan, Y. Xin, Nonlinear Dyn. 66, 575 (2011)

    Article  Google Scholar 

  20. D. Chakraboty, K.P. Das, J. Plasma Phys. 60, 151 (1998)

    Article  ADS  Google Scholar 

  21. E.F. El-Shamy, Chaos Solitons Fractals 25, 665 (2005)

    Article  ADS  MATH  Google Scholar 

  22. H. Schamel, Plasma Phys. 14, 905 (1972)

    Article  ADS  Google Scholar 

  23. A. Veksler, Y. Zarmi, Physica D 211, 57 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hashemite University, Zarqa, 13115, Jordan

    Fadi Awawdeh

  2. Department of Mathematics, Al al-Bayt University, Mafraq, 25113, Jordan

    H. M. Jaradat & S. Al-Shara’

Authors
  1. Fadi Awawdeh
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  2. H. M. Jaradat
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  3. S. Al-Shara’
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Correspondence to Fadi Awawdeh.

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Awawdeh, F., Jaradat, H.M. & Al-Shara’, S. Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma. Eur. Phys. J. D 66, 40 (2012). https://doi.org/10.1140/epjd/e2011-20518-0

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  • DOI: https://doi.org/10.1140/epjd/e2011-20518-0

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