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

Yıl 2022, Cilt: 6 Sayı: 2, 183 - 188, 30.12.2022
https://doi.org/10.46460/ijiea.1141361

Öz

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.

Kaynakça

  • 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

Yıl 2022, Cilt: 6 Sayı: 2, 183 - 188, 30.12.2022
https://doi.org/10.46460/ijiea.1141361

Öz

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.

Kaynakça

  • 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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Ebru Cavlak Aslan 0000-0002-2291-4044

Leyla Gürgöze 0000-0002-8316-5366

Yayımlanma Tarihi 30 Aralık 2022
Gönderilme Tarihi 28 Temmuz 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 6 Sayı: 2

Kaynak Göster

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, IJIEA. Aralık 2022;6(2):183-188. doi:10.46460/ijiea.1141361
Chicago Cavlak Aslan, Ebru, ve Leyla Gürgöze. “Soliton and Other Function Solutions of The Potential KdV Equation With Jacobi Elliptic Function Method”. International Journal of Innovative Engineering Applications 6, sy. 2 (Aralık 2022): 183-88. https://doi.org/10.46460/ijiea.1141361.
EndNote Cavlak Aslan E, Gürgöze L (01 Aralık 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 ve L. Gürgöze, “Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method”, ijiea, IJIEA, c. 6, sy. 2, ss. 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 (Aralık 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, IJIEA. 2022;6:183–188.
MLA Cavlak Aslan, Ebru ve Leyla Gürgöze. “Soliton and Other Function Solutions of The Potential KdV Equation With Jacobi Elliptic Function Method”. International Journal of Innovative Engineering Applications, c. 6, sy. 2, 2022, ss. 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, IJIEA. 2022;6(2):183-8.

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