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

Yıl 2022, , 183 - 188, 30.12.2022

Ebru Cavlak Aslan , Leyla Gürgöze

https://doi.org/10.46460/ijiea.1141361

Cited By: 1

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.

Anahtar Kelimeler

Jacobi elliptic function method, Soliton, The Potantial KdV equation

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

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.

Anahtar Kelimeler

Jacobi eliptic fonksiyon metod, Potansiyel KdV denklemi, Soliton

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.