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Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method

Year 2022, Volume: 6 Issue: 2, 183 - 188, 30.12.2022
https://doi.org/10.46460/ijiea.1141361

Abstract

The current study is concerned analytical solutions of the nonlinear potential KdV equation. Here, we implemented the Jacobi elliptic function method for soliton, hyperbolic and periodic solutions. Moreover, we illustrate our results with some graphs.

References

  • Referans 1 Boussinesq, J. (1871). Théorie de I’intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire, Comptes Rendus, 72, 755-759.
  • Referans 2 Korteweg, D.J.; de Vries G. (1895). On the change of from long waves advancing in a rectangular channel and on a new type of long stationary wave, Phil. Mag. 39(5), 422-443.
  • Referans 3 Constantin, A.; Henry, D. (2009). Solitons and Tsunamis, Z. Naturforsch, 64a, 65-68.
  • Referans4 Pandir, Y; Yildirim A. (2018). Analytical approach for the fractional differential equations by using the extended tanh method, Waves in Random and Complex Media, 3, 399-410.
  • Referans 5 Ghosh, A.; Maitra, S. (2021). The first integralmethod and some nonlinear models, Comput. Appl. Math., 40(79), 1-16.
  • Referans 6 Baskonus, H. M.; Bulut, H.; Sulaiman, T.A. (2019). New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method, Appl. Math. Nonl. Sci., 4(1), 129-138.
  • Referans7 Sedeeg, A,K; Nuruddeen, R.I; Gomez-Aguilar, J.F. (2019). Generalized optical soliton solutions to the (3+1) dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities, Optical Quant. Elec., 51(173), 1-15.
  • Referans 8 Ebaid, A.; Aly, E.H. (2012.). Exact solutions for the transformed reduced Ostrovsky equation via the F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions, Wave Motion, 49, 296-308.
  • Referans 9 Elboree, M.K. (2011). The Jacobi elliptic function method and its application for two component BKP hierarchy equations, Comput. Math. Appl., 62, 4402-4414.
  • Referans 10 Wang, G.W.; Xu, T.Z.; Ebadi, G.; Johnson, S.; Strong A.J. (2914). Singular solitons, shock waves, and other solutions to potential KdV equation, Nonl. Dyn., 76, 1059-1068.

Jacobi Eliptic Fonksiyon Metot ile Potansiyel KdV Denkleminin Soliton ve Diğer Fonksiyon Çözümleri

Year 2022, Volume: 6 Issue: 2, 183 - 188, 30.12.2022
https://doi.org/10.46460/ijiea.1141361

Abstract

Mevcut çalışma lineer olmayan potansiyel KdV denkleminin analitik çözümleri ile ilgilidir. Burada, biz soliton ve peryodik çözümleri elde edebilmek için Jacobi eliptik fonksiyon metodu uyguladık. Ayrıca sonuçlarımızı grafiklerle gösterdik.

References

  • Referans 1 Boussinesq, J. (1871). Théorie de I’intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire, Comptes Rendus, 72, 755-759.
  • Referans 2 Korteweg, D.J.; de Vries G. (1895). On the change of from long waves advancing in a rectangular channel and on a new type of long stationary wave, Phil. Mag. 39(5), 422-443.
  • Referans 3 Constantin, A.; Henry, D. (2009). Solitons and Tsunamis, Z. Naturforsch, 64a, 65-68.
  • Referans4 Pandir, Y; Yildirim A. (2018). Analytical approach for the fractional differential equations by using the extended tanh method, Waves in Random and Complex Media, 3, 399-410.
  • Referans 5 Ghosh, A.; Maitra, S. (2021). The first integralmethod and some nonlinear models, Comput. Appl. Math., 40(79), 1-16.
  • Referans 6 Baskonus, H. M.; Bulut, H.; Sulaiman, T.A. (2019). New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method, Appl. Math. Nonl. Sci., 4(1), 129-138.
  • Referans7 Sedeeg, A,K; Nuruddeen, R.I; Gomez-Aguilar, J.F. (2019). Generalized optical soliton solutions to the (3+1) dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities, Optical Quant. Elec., 51(173), 1-15.
  • Referans 8 Ebaid, A.; Aly, E.H. (2012.). Exact solutions for the transformed reduced Ostrovsky equation via the F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions, Wave Motion, 49, 296-308.
  • Referans 9 Elboree, M.K. (2011). The Jacobi elliptic function method and its application for two component BKP hierarchy equations, Comput. Math. Appl., 62, 4402-4414.
  • Referans 10 Wang, G.W.; Xu, T.Z.; Ebadi, G.; Johnson, S.; Strong A.J. (2914). Singular solitons, shock waves, and other solutions to potential KdV equation, Nonl. Dyn., 76, 1059-1068.
There are 10 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ebru Cavlak Aslan 0000-0002-2291-4044

Leyla Gürgöze 0000-0002-8316-5366

Publication Date December 30, 2022
Submission Date July 28, 2022
Published in Issue Year 2022 Volume: 6 Issue: 2

Cite

APA Cavlak Aslan, E., & Gürgöze, L. (2022). Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method. International Journal of Innovative Engineering Applications, 6(2), 183-188. https://doi.org/10.46460/ijiea.1141361
AMA Cavlak Aslan E, Gürgöze L. Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method. IJIEA. December 2022;6(2):183-188. doi:10.46460/ijiea.1141361
Chicago Cavlak Aslan, Ebru, and Leyla Gürgöze. “Soliton and Other Function Solutions of The Potential KdV Equation With Jacobi Elliptic Function Method”. International Journal of Innovative Engineering Applications 6, no. 2 (December 2022): 183-88. https://doi.org/10.46460/ijiea.1141361.
EndNote Cavlak Aslan E, Gürgöze L (December 1, 2022) Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method. International Journal of Innovative Engineering Applications 6 2 183–188.
IEEE E. Cavlak Aslan and L. Gürgöze, “Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method”, IJIEA, vol. 6, no. 2, pp. 183–188, 2022, doi: 10.46460/ijiea.1141361.
ISNAD Cavlak Aslan, Ebru - Gürgöze, Leyla. “Soliton and Other Function Solutions of The Potential KdV Equation With Jacobi Elliptic Function Method”. International Journal of Innovative Engineering Applications 6/2 (December 2022), 183-188. https://doi.org/10.46460/ijiea.1141361.
JAMA Cavlak Aslan E, Gürgöze L. Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method. IJIEA. 2022;6:183–188.
MLA Cavlak Aslan, Ebru and Leyla Gürgöze. “Soliton and Other Function Solutions of The Potential KdV Equation With Jacobi Elliptic Function Method”. International Journal of Innovative Engineering Applications, vol. 6, no. 2, 2022, pp. 183-8, doi:10.46460/ijiea.1141361.
Vancouver Cavlak Aslan E, Gürgöze L. Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method. IJIEA. 2022;6(2):183-8.

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