Skip to main content
SpringerLink
Log in

Analysis of Dust-Ion Acoustic Soliton and Shock Waves of Damped KdV Burgers’ Equation in Superthermal Plasmas: Adomian Decomposition Approach

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

Abstract

Present article deals with the study of approximate analytical solution of solitons and shock waves with the presence of acoustic dust-ion particles in the framework damped Korteweg-de Vries (DKdVB) Burgers’ model. The nonlinear KdVB equation with the existence of damping term has been computed with RPT and has been analysed by applying the well-known Adomian decomposition method (ADM). The essential idea of this proposed work is to analyse solitons and shock structures of the DKdVB which have not been obtained from regular approximate techniques. Initially, we employed ADM to find soliton solution of KdVB and have shown successful various soliton results. The DKdVB soliton results obtained from the Adomian decomposition scheme are compared with existing results and found to agree well. The results specify that the behaviour of DKdVB solitons increases for higher values of spectral index parameter and reduces for Mach number. The ADM soliton results further motivated to solve and analyse shock wave structures of DKdVB. The results of shock wave structures have been obtained explicitly by considering appropriate initial condition derived from the tanh method. The results of shock waves show the significant impact for varying values of damping parameter and viscosity coefficient. The proposed effort in this article would, in a way, illustrate the capability and efficiency of ADM to assess the numerous nonlinear propagations originating in the superthermal plasma.

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

Data Availability

The authors confirm that there is no associated data available for the above research work. Data sharing is not applicable to this article as no new data were created or analysed in this study.

References

  1. F.F. Chen, Introduction to plasma physics and controlled fusion (Plenum Press, Newyork, 1984)

    Book  Google Scholar 

  2. F. Verheest, Waves in dusty space plasma (Kunwer Press, 2007)

  3. A.A. Mamum, P.K. Shukla, Introduction to dust charge fluctuation (Cambridge University Press, 2002)

  4. N.N. Rao, P.K. Shukla, M.Y. Yu, Planet. Space Sci. 38, 543–546 (1990)

    Article  ADS  Google Scholar 

  5. M. Rosenberg, Planet. Space Sci. 41, 229–233 (1993)

    Article  ADS  Google Scholar 

  6. A.A. Mamun, P.K. Shukla, Phys. Plasmas 8, 3513–3516 (2001)

    Article  ADS  Google Scholar 

  7. A. Barkan, R.L. Merlino, N. D’Angelo, Phys. Plasmas, Phys. Plasmas 2, 3563-3565 (1995)

  8. J.H. Chu, J.B. Du, I. Lin, J. Phys. D: Appl. Phys. 27, 226 (1996)

    Google Scholar 

  9. P.K. Shukla, V.P. Silin, Phys. Scr. 45, 508 (1992)

    Article  ADS  Google Scholar 

  10. A. Barken, N. D’Angelo, R.L. Merlino, Planet Space Sci. 44, 239–242 (1996)

    Article  ADS  Google Scholar 

  11. R.L. Merlino, A. Barken, C. Thompsonand, N. D’Angelo, Phys. Plasmas 5, 1607–1614 (1998)

    Article  ADS  Google Scholar 

  12. V.N. Tsytovich, Phys. Uspekhi 40, 53 (1997)

    Article  ADS  Google Scholar 

  13. Y. Nakamura, H. Bailung, P.K. Shukla, Phys. Rev. Lett. 83, 1602 (1999)

    Article  ADS  Google Scholar 

  14. Q.-Z. Luo, N. D’Angelo, R.L. Merlino, Phys. Plasmas 6, 3455–3458 (1999)

    Article  ADS  Google Scholar 

  15. S.K. El-Labany, W.F. El-Taibany, Physics of Plasma 10, 4685–4695 (2010)

    Article  ADS  Google Scholar 

  16. P.K. Shukla, A.A. Mamun, IEEE Trans. Plasma Sci. 29, 221–225 (2001)

    Article  ADS  Google Scholar 

  17. X. Yang, C.-L. Wang, C. Liu, J.R. Zhang, Y.R. Shi, W.S. Duan, L. Yang, Phys. Plasmas 19, 103705 (2012)

    Article  ADS  Google Scholar 

  18. S. Maitra, G. Banerjee, Phys. Plasmas 21, 113707 (2014)

    Article  ADS  Google Scholar 

  19. J. Sarma, A.N. Dev, Indian J. Pure and Appl. Phys. 52, 747–754 (2014)

    Google Scholar 

  20. P. Chatterjee, R. Ali, A. Saha, Zeitschrift Für Naturforschung A 73, 151 (2018)

    Article  ADS  Google Scholar 

  21. S. Chowdhury, L. Mandi, P. Chatterjee, Phys. Plasmas 25, 042112 (2018)

    Article  ADS  Google Scholar 

  22. Q.L. Niu, M. Tian, H. Chen, AIP Advances 10, 095015 (2010)

    Article  ADS  Google Scholar 

  23. N. Paul, K.K. Mondal, R. Ali, P. Chatterjee, Indian J. Phys. 95, 2855–2863 (2021)

    Article  ADS  Google Scholar 

  24. N. Paul, K.K. Mondal, R. Ali, P. Chatterjee, Z. Naturforsch 74, 1–12 (2019)

    Article  Google Scholar 

  25. L. Mandi, K.K. Mondal, P. Chatterjee, Eur. Phys. J. Spec. Top. 228, 2753–2768 (2019)

    Article  Google Scholar 

  26. M.R. Hassan, S. Sultana, Contri. Plasma Phys. 61, e202100065 (2021)

    Google Scholar 

  27. P. Chatterjee, K. Roy, U.N. Ghosh Waves and Wave Interaction in Plasma (World Scientific Publishing Co. Pte. Ltd, 2023)

  28. J.K. Kevorkian, J.D. Cole, Multiple scale and singular perturbation methods (Springer Science and Business Media, 2012)

  29. J-H. He, Computer Method Appl. Mech. Eng., 178, 257-262 (1992)

  30. N. Faraz, Y. Khan, F. Austin, Zeitschrift fur Naturforschung A 65, 1055 (2014)

    Article  ADS  Google Scholar 

  31. S. Nadeem, N.S. Akbar, Commun. Nonlinear Sci. Num. Simul. 14, 3844–3855 (2009)

    Article  Google Scholar 

  32. G. Adomian, Nonlinear stochastic operator equations (Academic press, 2014)

  33. K. Abbaoui, Y. Cherruault 28, 103–109 (1994)

    MathSciNet  Google Scholar 

  34. G. Adomian, Appl. Math. Lett 1, 121–129 (1996)

    Google Scholar 

  35. D. Kaya, A. Yokus, Math. Comput. Simul. 60, 507–512 (2002)

    Article  Google Scholar 

  36. A.M. Wazwaz, Appl. Math. Comp. 102, 77–86 (1999)

    Article  MathSciNet  Google Scholar 

  37. H. Washimi, T. Taniuti, Phys. Rev. Let. 17, 996 (1996)

    Article  ADS  Google Scholar 

  38. I. Kourakis, S. Sultana, F. Verheest, Astrophys. Space. Sci. 338, 245–249 (2012)

    Article  ADS  Google Scholar 

  39. U.M. Abdelsalam, M.S. Zobaer, H. Akther, M.G.M. Ghazal, M.M. Fares, Acta Phys. Pol. Series A 137, 1061–1067 (2020)

    Article  ADS  Google Scholar 

  40. W. Malfliet, W. Hereman, Physica Scripta 54, 563 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  41. A.M. El-Hanbaly, E.K. El-Shewy, M. Sallah, H.F. Darweesh, Commun. Theor. Phys. 65, 606 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors wish to thank Prof. Prasanta Chatterjee, Department of Mathematics, Visva- Bharati, Santiniketan, West Bengal-731235, India, for his idea and help pertaining to this work. The authors also thank the anonymous reviewers for their insightful comments toward the betterment of the technical aspect of this article.

Author information

Author notes

  1. Mahesh Kumar and Ranjan Kumar Jana contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Indraprastha Institute of Information Technology Delhi, Delhi, 110020, India

    Mahesh Kumar

  2. Department of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat, 395507, Gujarat, India

    Ranjan Kumar Jana

Authors
  1. Mahesh Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ranjan Kumar Jana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ranjan Kumar Jana.

Ethics declarations

Conflict of Interest

The authors declare no competing interests.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, M., Jana, R.K. Analysis of Dust-Ion Acoustic Soliton and Shock Waves of Damped KdV Burgers’ Equation in Superthermal Plasmas: Adomian Decomposition Approach. Braz J Phys 54, 98 (2024). https://doi.org/10.1007/s13538-024-01468-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13538-024-01468-0

Keywords

Search

Navigation