Skip to main content
SpringerLink
Log in

Improved \(\tan \left (\frac {\Phi (\xi )}{2}\right )\)-Expansion Approach for Burgers Equation in Nonlinear Dynamical Model of Ion Acoustic Waves

  • General and Applied Physics
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

The main purpose of this research is to find new and more exact traveling wave solutions of nonlinear dynamical model of ion acoustic waves in plasma with the help of famous reductive perturbation technique. A well-known nonlinear evolution equation, namely Burgers equation, is derived to investigate ion acoustic waves in relativistic plasma containing electrons and positrons. The traveling wave solution of Burgers equation is carried out by an affective integration tool, namely improved \(\tan \left (\frac {\Phi (\xi )}{2}\right )\) expansion method. As a result, different types of solutions such as periodic, kink, rational, exponential function, and hyperbolic function, are obtained. The wave profiles of solitary wave solutions are graphically depicted. The algorithm of the suggested technique is also outlined. It is admitted that the used method is efficient and influential tool for constructing solitary wave solutions of nonlinear evolution equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. N. Raza, A. Zubair, . Commun. Theor. Phys. 71, 723 (2019)

    ADS  Google Scholar 

  2. N. Raza, U. Afzal, A.R. Butt, H. Rezazadeh, . Opt Quant Electron. 51, 107 (2019). https://doi.org/10.1007/s11082-019-1813-0

    Article  Google Scholar 

  3. U. Afzal, N. Raza, I. G. Murtaza, . Nonlinear Dyn. 95, 391 (2019)

    Google Scholar 

  4. Y. Nakamura, T. Ito, . K. Koga,. J. Plasma Phys. 49, 331 (1993)

    ADS  Google Scholar 

  5. H. Ikezi, R. J. Taylor, D.R. Baker, . Phys. Rev. Lett. 25, 11 (1970)

    ADS  Google Scholar 

  6. F. B. Rizzato, . J. Plasma Phys. 40, 289 (1988)

    ADS  Google Scholar 

  7. M.J. Rees. . (Cambridge University Press, New York, 1983)

    Google Scholar 

  8. C. Grabbe, . J. Geophys. Res. 94, 17,299–17,304 (1989)

    ADS  Google Scholar 

  9. M. Shahmansouri, M. Tribeche, . Astrophys Space Sci. 349, 781 (2014)

    ADS  Google Scholar 

  10. A. P. Lightman, A. A. Zdziarski, . Astrophys. J. 319, 643 (1987)

    ADS  Google Scholar 

  11. E. Tandberg-Hansen, A. G. Emslie. . (Cambridge University Press, New York, 1988)

    Google Scholar 

  12. F. C. Michel. . (University Press Chicago, Chicago, 1991)

    Google Scholar 

  13. J. Arons, . Space Sci. Rev. 24, 437 (1979)

    ADS  Google Scholar 

  14. M.L. Burns. . (American Institute of Physics, New York, 1983)

    Google Scholar 

  15. A. A. Mamun, P. K. Shukla, . Phys. Lett. A. 374, 472 (2010)

    ADS  Google Scholar 

  16. F. D. Steffen, M. H. Thoma, . Phys. Lett. B. 510, 98 (2001)

    ADS  Google Scholar 

  17. S. Singh, T. Honzawa, . Phys. Fluids B. 5, 2093 (1993)

    ADS  Google Scholar 

  18. H. K. Malik, S. Singh, R. P. Dahiya, . Phys. Plasmas. 1, 1137 (1994)

    ADS  Google Scholar 

  19. T. S. Gill, H. Kaur, N. S. Saini, . J. Plasma Phys. 71, 23 (2004)

    Google Scholar 

  20. M. G. Hafez, M. R. Talukder, Astrophys. Space Sci. 359(27) (2015)

  21. M. G. Hafez, M. R. Talukder, R. Rand Sakthivel, . Indian J. Phys. 90, 603 (2016)

    ADS  Google Scholar 

  22. M. G. Hafeza, M. R. Talukder, M. Hossain Ali, . Plasma Physics Reports. 43(4), 499 (2017)

    ADS  Google Scholar 

  23. A. Spitkovsky, . The Astrophys. J. 673, L39 (2008)

    ADS  Google Scholar 

  24. T. S. Gill, A. Singh, H. Kaur, N. S. Saini, P. Bala, . Phys. Lett. A. 361, 364 (2007)

    ADS  Google Scholar 

  25. T. S. Gill, A. S. Bains, N. S. Saini, . Can. J. Phys. 87, 861 (2009)

    ADS  Google Scholar 

  26. K. Roy, A. P. Misra, P. Chatterjee, . Phys. Plasmas. 15, 032310 (2008)

    ADS  Google Scholar 

  27. A. Shah, Q. Haque, S. Mahmood, . Astrophys. Space Sci. 335, 529 (2011)

    ADS  Google Scholar 

  28. H. R. Pakzad, M. Tribeche, . J. Fusion Energy. 32, 171 (2013)

    ADS  Google Scholar 

  29. M. R. Rouhani, Z. Ebne Abbasi, . Phys. Plasmas. 19, 112307 (2012)

    ADS  Google Scholar 

  30. H.R. Pakzad, . Phys. Lett. A. 373, 847 (2009)

    ADS  Google Scholar 

  31. N. Raza, A. Zubair, . Mod. Phy. Lett. B. 33, 1975 (2018)

    Google Scholar 

  32. N. Raza, A. Javid, . Waves Random Complex Media. 29, 496 (2019)

    ADS  MathSciNet  Google Scholar 

  33. N. Raza, A. Zubair, . Commun. Theor. Phys. 71, 723 (2019)

    ADS  Google Scholar 

  34. N. Raza, A. Javid, Mod. Phy. Lett. B. 33, 1850427 (10 pages) (2019)

  35. N. Raza, S. Sial, M. Kaplan, . Optik. 156, 628 (2018)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  37. C. Ablowitz. Solitons, Nonlinear Evolution Equation and Inverse Scattering (Cambridge University Press, New York, 1991)

    MATH  Google Scholar 

  38. M. Wang, Q. Zhou, . Phys. Lett. A. 216, 67 (1996)

    ADS  Google Scholar 

  39. Z. Feng, . J. Phys. A. 35(2), 343 (2002)

    ADS  MathSciNet  Google Scholar 

  40. A. M. Wazwaz, . Appl. Math. Comput. 154(3), 713 (2004)

    MathSciNet  Google Scholar 

  41. A. Shah, R. Saeed, . Phys. Lett. A. 373, 4164 (2009)

    ADS  Google Scholar 

  42. R. Saeed, A. Shah, M. Noaman-ul-Haq, . Phys. Plasmas. 17, 102301 (2010)

    ADS  Google Scholar 

  43. J. Manafian, M. Lakestani, . Optik. 127(4), 2040 (2016)

    ADS  Google Scholar 

  44. J. Manafian, M. Lakestani, . Optik. 127(20), 9603 (2016)

    ADS  Google Scholar 

  45. J. Manafian, R. Farshbaf Zinati, Proc. Natl. Acad. Sci., India, Sect. A. Phys. Sci. (2018)

  46. Y. Ugurlu, I.E. Inan, H. Bulut, . Optik. 131, 539 (2017)

    ADS  Google Scholar 

  47. U. Khan, A. Irshad, N. Ahmed, S.T. Mohyud-Din, . Optik Quant Electron. 50, 135 (2018)

    Google Scholar 

  48. J. Manafian, M. Lakestani, A. Bekir, . Int. J. A.pl. Comput. Math. 2, 243 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

    Nauman Raza & Jawad Afzal

  2. Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, Turkey

    Ahmet Bekir

  3. Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

Authors
  1. Nauman Raza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jawad Afzal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmet Bekir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hadi Rezazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmet Bekir.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raza, N., Afzal, J., Bekir, A. et al. Improved \(\tan \left (\frac {\Phi (\xi )}{2}\right )\)-Expansion Approach for Burgers Equation in Nonlinear Dynamical Model of Ion Acoustic Waves. Braz J Phys 50, 254–262 (2020). https://doi.org/10.1007/s13538-020-00743-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-020-00743-0

Keywords

Search

Navigation