SpringerLink
Log in

Soliton Solutions of Nonlinear Geophysical Kdv Equation Via Two Analytical Methods

  • Research
  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The new precise traveling wave solutions to the Geophysical KdV equation obtained by the \((\frac{G'}{G^2})\)-expansion method and Sine-Cosine method reflect the results for hyperbolic, trigonometric, and rational functions. Different physical wave shapes are displayed by all solutions, including the periodic, bright, and singular soliton solutions. Compared to the \((\frac{G'}{G^2})\)-expansion approach, the Sine-Cosine method is shown to be more straightforward, efficient, and involves less time-consuming symbolic computations, however the key factors of \((\frac{G'}{G^2})\)-expansion approach is that the great capacity of solutions can be obtained as more number parameters are involved in the solution procedure. The obtained results demonstrate the propagation of nonlinear tsunami structures, their interaction, and the progress of solitons. The propagation of nonlinear tsunami waves are shown to be strongly influenced by the travelling wave’s velocity and the Coriolis parameter.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Duran, S.: An investigation of the physical dynamics of a travelling wave solution called a bright soliton. Phys. Scr. 96(12), 125251 (2021). https://doi.org/10.1088/1402-4896/ac37a1

    Article  ADS  Google Scholar 

  2. Safari, M., Ganji, D.D., Moslemi, M.: Application of He’s variational iteration method and Adomian’s decomposition method to the fractional KdV-Burgers-Kuramoto equation. Comput. Math. Appl. 58(11–12), 2091–2097 (2009). https://doi.org/10.1016/j.camwa.2009.03.043

  3. Yao, S.W., Behera, S., Inc, M., Rezazadeh, H., Virdi, J.P.S., Mahmoud, W., Arqub, O.A., Osman, M.S.: Analytical solutions of conformable Drinfel’d-Sokolov-Wilson and Boiti Leon Pempinelli equations via sine-cosine method. Results Phys. 42, 105990 (2022). https://doi.org/10.1016/j.rinp.2022.105990

  4. Behera, S., Virdi, J.P.S.: Analytical solutions of some fractional order nonlinear evolution equations by sine-cosine method. Discontinuity Nonlinearity Complex. 11(2), 275–286 (2023). https://doi.org/10.5890/DNC.2023.06.004

    Article  Google Scholar 

  5. Wazwaz, A.M.: Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh-coth method. Appl Math Comput. 190(1), 633–640 (2007). https://doi.org/10.1016/j.amc.2007.01.056

  6. Behera, S.: Analysis of travelling wave solutions of two space-time nonlinear fractional differential equations by the first-integral method. Mod. Phys. Lett. B 38(4), 2350247 (2023). https://doi.org/10.1142/S0217984923502470

    Article  ADS  Google Scholar 

  7. Darvishi, M.T., Najafi, M., Wazwaz, A.M.: Some optical soliton solutions of space-time conformable fractional Schrödinger-type models. Phys. Scr. 96(6), 1–8 (2021). https://doi.org/10.1088/1402-4896/abf269

    Article  Google Scholar 

  8. Zayed, E.M.E., Al-Joudi, S., Applications of an extended \((\frac{G^{\prime }}{G})\)-expansion method to find exact solutions of nonlinear PDEs in mathematical physics, Math. Probl. Eng., 2010 (2010). https://doi.org/10.1155/2010/768573

  9. Behera, S., Virdi, J.S.: Some More Solitary Traveling Wave Solutions of Nonlinear Evolution Equations. Discontinuity Nonlinearity Complex. 12(1), 75–85 (2023). https://doi.org/10.5890/DNC.2023.03.006

    Article  Google Scholar 

  10. Bibi, S., Mohyud-Din, S.T., Ullah, R., Ahmed, N., Khan, U.: Exact solutions for STO and (3+ 1)-dimensional KdV-ZK equations using \((\frac{G^{\prime }}{G^2})\)-expansion method. Results Phys. 7, 4434–4439 (2017). https://doi.org/10.1016/j.rinp.2017.11.009

    Article  ADS  Google Scholar 

  11. Behera, S.: Dynamical solutions and quadratic resonance of nonlinear perturbed Schrödinger equation. Front. Appl. Math. Stat. 8, 128 (2023). https://doi.org/10.3389/fams.2022.1086766

    Article  ADS  Google Scholar 

  12. Behera, S., Mohanty, S., Virdi, J.P.S.: Analytical solutions and mathematical simulation of traveling wave solutions to fractional order nonlinear equations. Partial Differ. Equ. Appl. Math. 8, 100535 (2023). https://doi.org/10.1016/j.padiff.2023.100535

    Article  Google Scholar 

  13. D. J. Korteweg, G. deVries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. Ser. 39 422-443 (1895)

  14. Bhatta, D.D., Bhatti, M.I.: Numerical solution of KdV equation using modified Bernstein polynomials. Appl Math Comput. 174(2), 1255–1268 (2006). https://doi.org/10.1016/j.amc.2005.05.049

    Article  MathSciNet  Google Scholar 

  15. Kamyar, H., Akbulut, A.R.Z.U., Baleanu, D.U.M.I.T.R.U., Salahshour, S.O.H.E.I.L., Mirzazadeh, M., Akinyemi, L.: The geophysical KdV equation: its solitons, complexiton, and conservation laws. GEM-Int. J. Geomath. 13(1), 12 (2022). https://doi.org/10.1007/s13137-022-00203-8

    Article  MathSciNet  Google Scholar 

  16. Saifullah, S., Fatima, N., Abdelmohsen, S.A., Alanazi, M.M., Ahmad, S., Baleanu, D.: Analysis of a conformable generalized geophysical KdV equation with Coriolis effect. Alexandria Engineering Journal 73, 651–663 (2023). https://doi.org/10.1016/j.aej.2023.04.058

    Article  Google Scholar 

  17. Rizvi, S.T.R., Seadawy, A.R., Ashraf, F., Younis, M., Iqbal, H., Baleanu, D.: Lump and interaction solutions of a geophysical Korteweg-de Vries equation. Results Phys. 19, 103661 (2020). https://doi.org/10.1016/j.rinp.2020.103661

    Article  Google Scholar 

  18. Turgut, Ak., Saha, A., Dhawan. S., Kara, A.H., Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg-de Vries equation. Numer. Methods Partial Differ. Equ.,36(6), 1234–1253 (2020). https://doi.org/10.1002/num.22469

  19. Wang, K.L.: Novel approaches to fractional Klein-Gordon-Zakharov equation. Fractals 31(07), 2350095 (2023). https://doi.org/10.1142/S0218348X23500950

    Article  ADS  Google Scholar 

  20. Wang, K. L., Novel Investigation Of Fractional Long-And Short-Wave Interaction System. Fractals, 2450023 (2024). https://doi.org/10.1142/S0218348X24500233

  21. Wang, K.L.: New analysis methods for the coupled fractional nonlinear Hirota equation. Fractals 31(09), 1–14 (2023). https://doi.org/10.1142/S0218348X23501190

    Article  Google Scholar 

  22. Wang, K.L.: New Promising And Challenges Of The Fractional Calogeroâ€"Bogoyavlenskiiâ€"Schiff Equation. Fractals 31(09), 1–11 (2023). https://doi.org/10.1142/S0218348X23501104

  23. Wang, K.L.: Novel solitary wave and periodic solutions for the nonlinear Kaup-Newell equation in optical fibers. Opt. Quantum Electron. 56(4), 514 (2024). https://doi.org/10.1007/s11082-023-06122-8

    Article  Google Scholar 

  24. Wang, K. L., Novel perspective to the fractional schrödinger equation arising in optical fibers. Fractals, 2450034 (2024). https://doi.org/10.1142/S0218348X24500348

  25. Wei, C.F.: New solitary wave solutions for the fractional Jaulent-Miodek hierarchy model. Fractals 31(05), 2350060 (2023). https://doi.org/10.1142/S0218348X23500603

    Article  ADS  Google Scholar 

  26. Constantin, A., Henry, D.: Solitons and tsunamis. Z. Naturforsch 64(1–2), 65–68 (2009). https://doi.org/10.1515/zna-2009-1-211

    Article  ADS  Google Scholar 

  27. Lakshmanan, M., Solitons, Tsunamis and Oceanographical Applications of. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY, (2012). https://doi.org/10.1007/978-1-4614-1806-1_103

Download references

Author information

Authors and Affiliations

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

    Sidheswar Behera

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

    Noufe H. Aljahdaly

Authors
  1. Sidheswar Behera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Noufe H. Aljahdaly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sidheswar Behera.

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

Behera, S., Aljahdaly, N.H. Soliton Solutions of Nonlinear Geophysical Kdv Equation Via Two Analytical Methods. Int J Theor Phys 63, 107 (2024). https://doi.org/10.1007/s10773-024-05647-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-024-05647-2

Keywords

Search

Navigation