Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of the Coupled Potential Korteweg–de Vries (KdV) equation

Year 2019, Volume: 9 Issue: 1, 94 - 102, 30.06.2019

İbrahim Enam İnan

https://doi.org/10.31466/kfbd.542566

Cited By: 2

Abstract

In this article, some soliton wave solutions of
the coupled potential KdV equation have been found using the generalized (G '/
G) - expansion method. For this equation, hyperbolic function solutions,
trigonometric function solutions and rational function solutions have been
obtained. It was seen that the solutions provided the equation using
Mathematica 11.2 In addition, the graphic performances of some solutions are
given

Keywords

The coupled potential KdV-equation, Soliton wave solutions, Generalized (G'/G)- expansion method

Potansiyel KdV- denklem çiftinin bazı soliton dalga çözümleri için Genelleştirilmiş (G'/G)- açılım metodu

Abstract

Bu makalede, genelleştirilmiş (G '/ G) – açılım metodu
kullanılarak potansiyel KdV denklem çiftinin bazı soliton dalga çözümleri
bulunmuştur. Bu denklem için hiperbolik fonksiyon çözümleri, trigonometrik
fonksiyon çözümleri ve rasyonel fonksiyon çözümleri elde edilmiştir. Çözümlerin
Mathematica 11.2 kullanılarak denklemi sağladığı görülmüştür. Ayrıca, bazı
çözümlerin grafik performansları verilmiştir.

Keywords

Potansiyel KdV- denklem çifti, Soliton dalga çözümleri, Genelleştirilmiş (G'/G)- açılım metodu

References

• Bock, T.L. and Kruskal, M.D. (1979). “A two-parameter Miura transformation of the Benjamin-Ono equation”, Physics Letters A, 74 , 173-176.
• Cariello, F. and Tabor, M. (1989).“Painleve expansions for nonintegrable evolution equations”, Physica D, 39, 77-94.
• Chen, H. T. and Hong-Qing, Z. (2004). “New double periodic and multiple soliton solutions of the generalized (2+1)-dimensional Boussinesq equation”, Chaos Solitons and Fractals, 20, 765-769.
• Chen, Y., Wang, Q. and Li, B. (2004). “Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations”, Zeitschrift für Naturforschung A, 59, 529-536.
• Chen, Y. and Yan, Z. (2006) .“The Weierstrss elliptic function expansion method and its applications in nonlinear wave equations”, Chaos Solitons and Fractals, 29, 948-964.
• Chuntao, Y. (1996). “A simple transformation for nonlinear waves”, Physics Letters A, 224, 77-84.
• Chen, H. and Zhang H., (2004). “New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation”, Chaos Solitons and Fractals, 19, 71-76.
• Clarkson, P.A. (1989). “New similarity solutions for the modified boussinesq equation”, Journal of Physics A: Mathematical and General, 22, 2355-2367.
• Elwakil, S. A., El-labany, S.K., Zahran, M.A. and Sabry, R. (2002). “Modified extended tanh-function method for solving nonlinear partial differential equations”, Physics Letters A, 299, 179-188.
• Fan, E. (2000). “Two new application of the homogeneous balance method”, Physics Letters A, 265, 353-357.
• Fan, E. (2000). ”Extended tanh-function method and its applications to nonlinear equations”, Physics Letters A, 277, 212-218.
• Fu, Z., Liu S. And Zhao, Q. (2001). “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations”, Physics Letters A, 290, 72-76.
• Guo, S. and Zhou, Y. (2010) .“The extended -exnsion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations”, Applied Mathematics and Computation, 215, 3214-3221.
• Khater, M.M.A. (2015). “Extended Exp(−𝜑(ξ))-Expansion Method for Solving the Generalized Hirota-Satsuma Coupled KdV System”, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 15, 7, Version 1.0.
• Li, L., Li, E. and Wang, M. (2010).“The -expansion method and its application to travelling wave solutions of the Zakharov equations”, Applied Mathematics-A Journal of Chinese Universities, 25, 454-462.
• Lü, H. L., Liu, X. Q. and Niu, L. (2010) .“A generalized -expansion method and its applications to nonlinear evolution equations”, Applied Mathematics and Computation, 215, 3811-3816.
• Malfliet, W. (1992).“Solitary wave solutions of nonlinear wave equations”, American Journal of Physics, 60, 650-654.
• Manafian, J. (2016). “Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan – expansion Method”, Optik, 127, 4222-4245.
• Manafian, J., Aghdaei, M.F., Khalilian, M. and Jeddi, R.S. (2017) .“Application of the generalized -expansion method for nonlinear PDEs to obtaining soliton wave solution”, Optik, 135, 395–406.
• Shen, S. and Pan, Z. (2003). “A note on the Jacobi elliptic function expansion method”, Physics Letters A, 308, 143-148.
• Wang, M., Li, X. and Zhang, J. ( 2008) .“The -expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics”, Physics Letters A, 372, 417-423.
• Yan, Z. (2001).“New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations”, Physics Letters A, 292, 100-106.