Skip to main content
SpringerLink
Log in

Nonlinear evolution equations and their traveling wave solutions in fluid media by modified analytical method

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

This investigation proposes the novelty of the modified \((\frac{G'}{G^2})\)-expansion method to look for new exact traveling wave solutions to two important nonlinear evolution equations such as the Konno–Oono equation and the Boussinesq equation. The simplicity and dependability of this approach make it advantageous for solving nonlinear issues. The technique involves wave transformation to get the nonlinear evolution equation down to the corresponding ordinary differential equations. The solutions include some new exact traveling solutions and are categorized into three classes of trigonometric, hyperbolic, and rational solutions. Numerical simulation is used to support the solutions and give them physical meaning. These results contain a large number of travelling wave solutions that are crucial for explaining certain scientific phenomena in fluid media.

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

Similar content being viewed by others

References

  1. I Loutsenko and D Roubtsov, Phys. Rev. Lett. 78, 3011 (1997)

    Article  ADS  Google Scholar 

  2. T Das, U Ghosh, S Sarkar and S Das, Pramana – J. Phys. 93, 76 (2019)

    Google Scholar 

  3. S Duran, Physica Scripta 96(12), 125251 (2021)

    Article  ADS  Google Scholar 

  4. R Camassa and D D Holm, Phys. Rev. Lett. 71, 1661 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  5. A M Wazwaz, Pramana – J. Phys. 87, 68 (2016)

    Google Scholar 

  6. S Duran and D Kaya,  Eur. Phys. J. Plus 136(9), 1 (2021)

    Article  Google Scholar 

  7. N H Aljahdaly and S A El-Tantawy, Mathematics  9, 432 (2021)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. S Behera and J P S Virdi, Authorea (2020)

  10. S Behera and J P S Virdi, Proceedings of the Seventh International Conference on Mathematics and Computing, Advances in Intelligent Systems and Computing 1412 (2022)

  11. M Safari, D D Ganji and M Moslemi, Computers Math. Appl. 58, 2091 (2009)

    Google Scholar 

  12. S Duran and D Kaya, Erzincan Univ. J. Sci. Technol. 14(3), 898 (2021)

    Google Scholar 

  13. R M El-Shiekh, CAMWA 73, 1414 (2017)

    MathSciNet  Google Scholar 

  14. M M Miah, H M S Ali, M A Akbar and A M Wazwaz, Eur. Phys. J. Plus 132, 252 (2017)

    Article  Google Scholar 

  15. N H Aljahdaly, A R Seadawy and W A Albarakati, Mod. Phys. Lett. B 34, 2050279 (2020)

    Article  ADS  Google Scholar 

  16. N A Kudryashov, Regular and Chaotic Dynamics 23, 471 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  17. G Nhawu, P Mafuta and J Mushanyu, J. Math. Comput. Sci. 3, 307 (2016)

    Google Scholar 

  18. N Bildik and A Konuralp, Int. J. Non. Sci. Num. Simul. 7, 65 (2006)

    Google Scholar 

  19. M Wang, X Li, J Zhang, Phys. Lett. A  372(4), 417 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  20. C Bian, J Pang, L Jin and X Ying, Comm. Non. Sci. Numer. Simul. 15, 2337 (2010)

    Article  ADS  Google Scholar 

  21. E M E Zayed and S Al-Joudi, Math. Problems in Engineering 2010 (2010)

  22. E Fan and J Zhang, Phys. Lett. A 305(16), 383 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  23. S Behera, N H Aljahdaly and J P S Virdi, J. Ocean Engg. Sci. 7(4), 313 (2022)

    Article  Google Scholar 

  24. N H Aljahdaly, Results Phys. 13, 102272 (2019)

    Article  Google Scholar 

  25. K Konno and H Oono, J. Phys. Soc. Japan 63, 377 (1994)

    Article  ADS  Google Scholar 

  26. Z F Kocaka, H Bulutb, D A Koca and H M Baskonusc, Optik 127, 10786 (2016)

    Article  ADS  Google Scholar 

  27. G Yel, H M Baskonus, H Bulut, Opt. Quant. Elect. 49, 285 (2017)

    Article  Google Scholar 

  28. J Manafian, I Zamanpour and A Ranjbaran, J. Phys. Commun. 2, 015023 (2018)

  29. K Konno and H Kakuhata, J. Phys. Soc. Japan 65, 713 (1996)

    Article  ADS  Google Scholar 

  30. W W Mohammed, N Iqbal, A Ali and M El-Morshedy, Results Phys. 21, 103830 (2021)

    Article  Google Scholar 

  31. S Duran, ADYU J. Sci. 10(2), 585 (2020)

    Google Scholar 

  32. M Alizamini, S Mehdi, H Rezazadeh, K Srinivasa and A Bekir, Pramana – J. Phys. 94, 1 (2020)

    Google Scholar 

  33. A M Wazwaz, Appl. Math. Computation 192, 479 (2007)

    Article  MathSciNet  Google Scholar 

  34. A M Wazwaz, Chaos Soliton. Fract. 12, 1549 (2001)

    Article  ADS  Google Scholar 

  35. M L Gandarias and M S Bruzon, J. Nonlinear Math. Phys. 5(1) 8 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  36. Y L Ma and B Q Li, Appl. Math. Lett. 124, 107677 (2022)

    Article  Google Scholar 

  37. S Kumar, S Malik, H Rezazadeh and L Akinyemi, Nonlinear Dynamics 107(3), 2703 (2022)

    Article  Google Scholar 

  38. B Q Li, A M Wazwaz, Y L Ma, Chinese J. Phys. 77, 1782 (2022)

    Google Scholar 

  39. E W Weisstein, Concise Encyclopedia of Mathematics, 2nd ed. (CRC Press, New York, 2002)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Veer Surendra Sai University of Technology, Burla, 768 018, India

    S Behera

  2. Department of Mathematics, Faculty of Sciences and Arts-Rabigh Campus, King Abdulaziz University, Jeddah, Saudi Arabia

    N H Aljahdaly

Authors
  1. S Behera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N H Aljahdaly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S Behera.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Behera, S., Aljahdaly, N.H. Nonlinear evolution equations and their traveling wave solutions in fluid media by modified analytical method. Pramana - J Phys 97, 130 (2023). https://doi.org/10.1007/s12043-023-02602-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-023-02602-4

Keywords

PACS Nos

Search

Navigation