SavedAdd your journal

Journals / Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi / 2021 / Cilt: 8 - Sayı: 1

Exact Solutions of the Benney–Luke Equation via (1/G')- Expansion Method

(1/G')-Açılım Yöntemi ile Benney-Luke Denkleminin Tam Çözümleri

Hülya DURUR
Asıf YOKUŞ
Pages
56–64
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Results show that the(1/ ) G - expansion method provides an efficient and straightforward mathematical instrument for finding solutions ofnonlinear evolution equations (NLEEs).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the(1/ ) G -expansion method was implemented to solve the Benney–Luke (BL) equation.
📊
Key Findings & Data:The solutions obtained from the BL equation were inhyperbolic form. 3D, 2D and contour graphs of obtained solutions are presented.
💡
Conclusion & Impact:Results show that the(1/ ) G - expansion method provides an efficient and straightforward mathematical instrument for finding solutions ofnonlinear evolution equations (NLEEs).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, the(1/ ) G -expansion method was implemented to solve the Benney–Luke (BL) equation. Exactsolutions of the BL equation were obtained via this method. The solutions obtained from the BL equation were inhyperbolic form. 3D, 2D and contour graphs of obtained solutions are presented. Results show that the(1/ ) G - expansion method provides an efficient and straightforward mathematical instrument for finding solutions ofnonlinear evolution equations (NLEEs).

Özet

Bu çalışmada, Benney-Luke (BL) denklemini çözmek için(1/ ) G -açılım yöntemi uygulanmıştır. BLdenkleminin tam çözümleri bu yöntem ile elde edilmektedir. BL denkleminden elde edilen çözümler hiperbolikformdadır. Elde edilen çözümlerin 3 boyutlu, 2 boyutlu ve kontur grafikleri sunulmaktadır. Sonuçlar,(1/ ) G - açılım yönteminin doğrusal olmayan evrim denklemlerinin çözümlerini bulmak için etkili ve basit birmatematiksel enstrüman olduğu gösterilmiştir.

🔖

Cite This Article

DURUR, H., YOKUŞ, A. (2022). Exact Solutions of the Benney–Luke Equation via (1/G')- Expansion Method. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, Cilt: 8 - Sayı: 1, 56–64. https://ajindex.com/articles/464231

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. Kheiri, H., Alipour, N. & Dehghani, R. (2011). Homotopy analysis and Homotopy-Pade methods for the modified Burgers-Korteweg-de-Vries and the Newell Whitehead equation. Mathematical Sciences, 5(1), 33- 50
  2. Durur, H. (2020). Different Types Analytic Solutions of the (1+1)-Dimensional Resonant Nonlinear Schrödinger’s Equation Using (G′/G)-Expansion Method. Modern Physics Letters B, 34(03), 2050036
  3. Ahmad H., Rafiq, M., Cesarano, C. & Durur, H. (2020). Variational Iteration Algorithm-I with an Auxiliary Parameter for Solving Boundary Value Problems. Earthline Journal of Mathematical Sciences (ISSN: 2581- 8147), 3(2), 229-247
  4. Duran, S. (2020). Solitary Wave Solutions of the Coupled Konno-Oono Equation by using the Functional Variable Method and the Two Variables (G'/G, 1/G)-Expansion Method. Adıyaman Üniversitesi Fen Bilimleri Dergisi, 10(2), 585-594
  5. Yavuz, M. & Özdemir, N. (2018). An Integral Transform Solution for Fractional Advection-Diffusion Problem. Mathematical Studies and Applications, 4-6, 442
  6. Yokus, A., Durur, H., Ahmad, H., Thounthong, P. & Zhang, Y. F. (2020). Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G′/G, 1/G)-expansion and (1/G′)-expansion techniques. Results in Physics, 19, 103409
  7. Yokus, A., Durur, H. & Ahmad, H. (2020). Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system. Facta Universitatis, Series: Mathematics and Informatics, 35(2), 523-531
  8. Durur, H. & Yokuş, A. (2020) Vakhnenko-Parkes Denkleminin Hiperbolik Tipte Yürüyen Dalga Çözümü. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 13(2), 550-556
  9. Yokus, A., Durur, H., Ahmad, H. & Yao, S. W. (2020). Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics, 8(6), 908
  10. Su-Ping, Q. & Li-Xin, T. (2007). Modification of the Clarkson–Kruskal Direct Method for a Coupled System. Chinese Physics Letters, 24(10), 2720
  11. Yokuş, A. & Kaya, D. (2020). Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics. International Journal of Modern Physics B, 34(29), 2050282
  12. Yavuz, M. & Özdemir, N. (2018). A Quantitative Approach to Fractional Option Pricing Problems with Decomposition Series. Konuralp Journal of Mathematics, 6(1), 102-109
  13. Rady, A. A., Osman, E. S. & Khalfallah, M. (2010). The Homogeneous Balance Method and Its Application to the Benjamin–Bona–Mahoney (BBM) Equation. Applied Mathematics and Comp