Variant Bussinesq Denklemlerinin Hareket Eden Dalga Çözümleri için Tan F ξ /2 Açılım Metodu

Bu makalede farklı Bussinesq denklemlerinin hareket eden dalga çözümleri için tan F ξ /2 açılım metodu sunulmuştur. Bu denklem için hiperbolik fonksiyon çözümü, trigonometric fonksiyon çözümü, üstel fonksiyon çözümü ve rasyonel çözüm elde edilmiştir. Son zamanlarda, bu metot lineer olmayan kısmi diferensiyel denklemlerin hareket eden dalga çözümlerinin elde edilmesi için bilim adamları tarafından çalışılmaktadır

Anahtar Kelimeler:

Üstel fonksiyon çözüm, Hiperbolik fonksiyon çözüm, Rasyonel çözüm, Tan F ξ /2 açılım metodu, Variant Bussinesq denklemleri, Trigonometric fonksiyon çözüm

Tan -Expansion Method for Traveling Wave Solutions of the Variant Boussinesq Equation

In this paper, we implemented a tan -expansion method for the traveling wave solutions of the variant Boussinesq equation. We have hyperbolic function solution, trigonometric function solution, exponential solution and rational solution for this equation. Recently, this method has been studied for obtaining traveling wave solutions of nonlinear partial differential equations by sciences.

Keywords:

The variant Boussinesq equation, tan -expansion method, hyperbolic function solution, trigonometric function solution, exponential solution, rational solution,

PDF

___

1. Hu, XB., Ma, WX. 2002. Application of Hirota’s bilinear formalism to the Toeplitz lattice-some special soliton-like solutions, Phys. Let. A, 293: 161-165.
2. Shang, Y. 2007. Bäcklund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation, Appl Math Comput, 187: 1286-1297.
3. Abourabia, AM., El Horbaty, MM. 2006. On solitary wave solutions for the two-dimensional nonlinear modified Kortweg–de Vries–Burger equation, Chaos Soliton Fract, 29: 354-364.
4. Bock, TL., Kruskal, MD. 1979. A two-parameter Miura transformation of the Benjamin-Ono equation, Phys. Let. A, 74: 173-176.
5. Drazin, PG., Jhonson, RS. 1989. Solitons: An Introduction, Cambridge University Press, Cambridge.
6. Matveev, VB., Salle, MA. 1991. Darboux transformations and solitons, Springer, Berlin.
7. Cariello, F., Tabor, M. 1989. Painlevé expansions for nonintegrable evolution equations, Physica D, 39: 77-94.
8. Fan, E. 2000. Two new applications of the homogeneous balance method, Phys. Let. A, 265: 353-357.
9. Clarkson, PA. 1989. New Similarity Solutions for the Modified Boussinesq Equation, J Phys A-Math Gen, 22: 2355- 2367.
10. Chuntao, Y. 1996. A simple transformation for nonlinear waves, Phys. Let. A, 224: 77-84.
11. Malfliet, W. 1992. Solitary wave solutions of nonlinear wave equations, Am J Phys, 60: 650-654.
12. Fan, E. 2000. Extended tanh-function method and its applications to nonlinear equations, Phys. Let. A, 277: 212-218.
13. Elwakil, SA., El-labany, SK., Zahran, MA., Sabry, R. 2002. Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Let. A, 299: 179- 188.
14. Chen, H., Zhang, H. 2004. New multiple soliton solutions to the general Burgers-Fisher equation and the KuramotoSivashinsky equation, Chaos Soliton Fract, 19: 71-76.
15. Fu, Z., Liu, S., Liu, S., Zhao, Q. 2001. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Let. A, 290: 72-76.
16. Shen S., Pan, Z. 2003. A note on the Jacobi elliptic function expansion method, Phys. Let. A, 308: 143-148.
17. Chen, HT., Hong-Qing, Z. 2004. New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation, Chaos Soliton Fract, 20: 765-769.
18. Chen, Y., Wang, Q., Li, B. 2004. Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations, Z Naturforsch A, 59: 529-536.
19. Chen, Y., Yan, Z. 2006. The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations. Chaos Soliton Fract, 29: 948-964.
20. Wang, M., Li, X., Zhang, J. 2008. The G Gl a k-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Let. A, 372: 417-423.
21. Guo, S., Zhou, Y. 2010. The extended G Gl a k-expansion method and its applications to the Whitham–Broer–Kaup– Like equations and coupled Hirota–Satsuma KdV equations, Appl Math Comput, 215: 3214-3221.
22. Lü, HL., Liu, XQ., Niu, L. 2010. A generalized G Gl a k -expansion method and its applications to nonlinear evolution equations, Appl Math Comput, 215: 3811–3816.
23. Li, L., Li, E., Wang, M. 2010. The , G G G l 1 a k-expansion method and its application to travelling wave solutions of the Zakharov equations, Applied Math-A J Chinese U, 25, 454 - 462.
24. Manafian, J. 2016. Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan(Φ(ξ)/2)- expansion method, Optik, 127: 4222-4245.
25. Fan, E. 2000. Two new applications of the homogeneous balance method, Phys. Let. A 265: 353–357.
26. Yuan, W., Meng, F., Huang, Y., Wu, Y. 2015. All traveling wave exact solutions of the variant Boussinesq equations Appl Math Comput, 268: 865–872.
27. Guo, P., Wu, X., Wang, L. 2015. Multiple soliton solutions for the variant Boussinesq equations, Adv Differ Equ-Ny, 2015: 37.
28. Khan, K., Akbar, MA. 2014. Study of analytical method to seek for exact solutions of variant Boussinesq equations, Springerplus, 3: 324.