Skip to main content
SpringerLink
Log in

Ion-acoustic solitary wave solutions of nonlinear damped Korteweg–de Vries and damped modified Korteweg–de Vries dynamical equations

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

By using the reductive perturbation technique, the nonlinear dust ion-acoustic solitary wave models of the damped Korteweg–de Vries (D-KdV) and modified damped Korteweg–de Vries (D-mKdV) equations are formulated. We constructed the more general and new solitary wave solutions of nonlinear damped KdV and damped mKdV equations by using the modified mathematical technique. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of adiabatic parameters, dynamics of fluid and problems of biomedical, industrial phenomena. The new solutions are obtained in the shape of dark solitons, bright solitons, traveling wave and kink and anti-kink wave solitons. We show the physical structure of new solutions by two and three-dimensions graphical to know the physical interpretation of different structure of dust ion-acoustic solitary wave. The calculations show that this new technique is more powerful, effective, straightforward, and fruitfulness to study analytically other nonlinear complex physical models in plasma physics, mathematical physics, fluid mechanics, hydrodynamics, mathematical biology and many other physical sciences.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. F Verheest Waves in Dusty Space Plasmas (Dordrecht: Kluwer Academic) (2000)

    Google Scholar 

  2. P K Shukla and A A Mamun Introduction to Dusty Plasma Physics, Institute of Physics Bristol (2002)

  3. A Barkan, N DAngelo and R L Merlino Planet. Planet. Space Sci. 44 239 (1996)

    ADS  Google Scholar 

  4. A Bouchoule Dusty Plasmas (New York: Wiley) (1999)

    Google Scholar 

  5. X Wang, X Bhattacharjee, S K Gou and J Goree Phys. Plasmas 8 5018 (2001).

    ADS  Google Scholar 

  6. D A Mendis Plasma Sources Sci. Technol. 11 219 (2002)

    ADS  Google Scholar 

  7. S K El-Labany, E F El-Shamy and S A El-Warraki Astrophys. Space Sci. 315 287 (2008)

    ADS  Google Scholar 

  8. S K El-Labany, M Shalaby, E F El-Shamy and L S El-Sherif Planet. Space Sci. 57 1246 (2009)

    ADS  Google Scholar 

  9. P K Shukla and V P Silin Physica Scr. 45 508 (1992)

    ADS  Google Scholar 

  10. A Barkan, R L Merlino and N D’angelo Phys. Plasmas 2 3563 (1995)

    ADS  Google Scholar 

  11. S Maitra and G Banerjee Phys. Plasmas 21 113707 (2014)

    ADS  Google Scholar 

  12. M Tribeche and T H Zerguini Phys. Plasmas 8 394 (2001)

    ADS  Google Scholar 

  13. A V Volosevich and C V Meister Contrib. Plasma Phys. 42 61 (2002)

    ADS  Google Scholar 

  14. Z Zhao and L He Appl. Math. Lett., 95 114 (2019)

    MathSciNet  Google Scholar 

  15. Z Zhao Appl. Math. Lett. 89 103 (2019)

    MathSciNet  Google Scholar 

  16. Z Zhao and B Han Nonlinear Dyn., 94 461 (2018)

    Google Scholar 

  17. Z Zhao Anal. Math. Phys., 9 119 (2019)

    MathSciNet  Google Scholar 

  18. I Aslan and T Ozis Appl. Math. Comput. 209 425 (2009)

    MathSciNet  Google Scholar 

  19. T Ozis and I Aslan Commun. Theor. Phys. 51 577 (2009)

    Google Scholar 

  20. I Aslan and T Ozis Appl. Math. Comput. 211 531 (2009)

    MathSciNet  Google Scholar 

  21. I Aslan Appl. Math. Comput. 215 857 (2009)

    MathSciNet  Google Scholar 

  22. I Aslan Comput. Math. Appl. 59 2896 (2010)

    MathSciNet  Google Scholar 

  23. A Seadawy, D Lu and M Arshad Indian J. Phys. 93 1041 (2019)

    ADS  Google Scholar 

  24. R Shahein and A seadawy Indian J. Phys. 93 (2019) 941-949

    ADS  Google Scholar 

  25. A seadawy and N Cheemaa Indian J. Phys. (2019), https://doi.org/10.1007/s12648-019-01442-6

  26. A R Seadawy, M Iqbal and D Lu Indian J. Phys. (2019). https://doi.org/10.1007/s12648-019-01500-z

  27. A R Seadawy, M Iqbal and D Lu Indian J. Phys. (2019). https://doi.org/10.1007/s12648-019-01532-5

  28. W M Moslem and W F El-Taibany Phys. Plasmas 12 122309 (2005)

    ADS  Google Scholar 

  29. M Shalaby, S K El-Labany, E F El-Shamy and M A Khaled Astrophys. Space Sci. 326 273 (2010)

    ADS  Google Scholar 

  30. S K El-Labany, W M Moslem and A E Mowafy Phys. Plasmas 10 4217 (2003)

    ADS  Google Scholar 

  31. R L Merlino J. Plasma Phys. 80 773 (2014)

    ADS  Google Scholar 

  32. J Tamang, K Sarkar and A Saha Physica A 505 18 (2018)

    ADS  MathSciNet  Google Scholar 

  33. A R Seadawy and J Manafian Results Phys. 8 1158 (2018)

    ADS  Google Scholar 

  34. A R Seadawy and K El-Rashidy Math. Comput. Model 57 1371 (2013)

    Google Scholar 

  35. M Arshad, A R Seadawy and D Lu Results Phys. 13 102305 (2019)

    Google Scholar 

  36. A R Seadawy and D Lu Results Phys. 6 590 (2016)

  37. A R Seadawy Appl. Math. Sci. 82 4081 (2012)

    MathSciNet  Google Scholar 

  38. M Iqbal, A R Seadawy and D Lu Modern Phys. Lett. A 33 1850183 (2018)

    ADS  MathSciNet  Google Scholar 

  39. M Iqbal, A R Seadawy and D Lu Modern Phys. Lett. A 233 1765 (2018)

    Google Scholar 

  40. A R Seadawy, D Lu and M Iqbal Pramana 93 10 (2019)

  41. M Iqbal, A R Seadawy and D Lu Modern Phys. Lett. B 14 1950210 (2019)

    Google Scholar 

  42. A R Seadawy Comput. Math. Appl. 67 172 (2014)

  43. A R Seadawy Phys. Plasmas 21 052107 (2014)

    ADS  Google Scholar 

  44. A R Seadawy Eur. Phys. J. Plus 130 9 (2015)

  45. I Ahmed, A R Seadawy and D Lu Eur. Phys. J. Plus 134 120 (2019)

    ADS  Google Scholar 

  46. A R Seadawy and K El-Rashidy Sci. World J. 724759 (2014)

  47. A R Seadawy and N Cheemaa Indian J. Phys. 10 (2019)

  48. N Nasreen, A R Seadawy, D Lu and M Arshad Results Phys. 102263 (2019)

  49. D Lu, A R Seadawy and M Iqbal Results Phys. 11 1161 (2018)

    ADS  Google Scholar 

  50. D Lu, A R Seadawy and M Iqbal Open Phys. 16 896 (2018)

    ADS  Google Scholar 

  51. N D’angelo Phys. Plasmas 5 3155 (1998)

    ADS  Google Scholar 

  52. S Ghosh J. Plasma Phys. 71 519 (2005)

    ADS  Google Scholar 

  53. E Infeld and G Rowlands (Cambridge: Cambridge University Press) (1990)

  54. H Washimi and T Taniuti Phys. Rev. Lett. 19 996 (1966)

    ADS  Google Scholar 

  55. S K El-Labany and E F El-Shamy Phys. Plasmas 12 042301 (2005)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

  2. Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Aly R. Seadawy, Mujahid Iqbal & Dianchen Lu

Authors
  1. Aly R. Seadawy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mujahid Iqbal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dianchen Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Aly R. Seadawy or Dianchen Lu.

Ethics declarations

Conflict of interest

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The authors did not have any competing interests in this research.

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

Seadawy, A.R., Iqbal, M. & Lu, D. Ion-acoustic solitary wave solutions of nonlinear damped Korteweg–de Vries and damped modified Korteweg–de Vries dynamical equations. Indian J Phys 95, 1479–1489 (2021). https://doi.org/10.1007/s12648-019-01645-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-019-01645-x

Keywords

PACS Nos.

Search

Navigation