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.
Tan (F(ξ)/2)-Expansion Method for Traveling Wave Solutions of the Variant Bussinesq Equations
In this paper, we implemented a tan (F(ξ)/2)-expansion method for the traveling wave solutions of the variant Bussinesq equations.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.
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- 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.
- Shang, Y. 2007. Bäcklund transformation, Lax pairs and
explicit exact solutions for the shallow water waves equation,
Appl Math Comput, 187: 1286-1297.
- 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.
- Bock, TL., Kruskal, MD. 1979. A two-parameter Miura
transformation of the Benjamin-Ono equation, Phys. Let. A,
74: 173-176.
- Drazin, PG., Jhonson, RS. 1989. Solitons: An Introduction,
Cambridge University Press, Cambridge.
- Matveev, VB., Salle, MA. 1991. Darboux transformations
and solitons, Springer, Berlin.
- Cariello, F., Tabor, M. 1989. Painlevé expansions for
nonintegrable evolution equations, Physica D, 39: 77-94.
- Fan, E. 2000. Two new applications of the homogeneous
balance method, Phys. Let. A, 265: 353-357.
- Clarkson, PA. 1989. New Similarity Solutions for the
Modified Boussinesq Equation, J Phys A-Math Gen, 22: 2355-
2367.
- Chuntao, Y. 1996. A simple transformation for nonlinear
waves, Phys. Let. A, 224: 77-84.
- Malfliet, W. 1992. Solitary wave solutions of nonlinear wave
equations, Am J Phys, 60: 650-654.
- Fan, E. 2000. Extended tanh-function method and its
applications to nonlinear equations, Phys. Let. A, 277: 212-218.
- 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.
- 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.
- 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.
- Shen S., Pan, Z. 2003. A note on the Jacobi elliptic function
expansion method, Phys. Let. A, 308: 143-148.
- 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.
- 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.
- Chen, Y., Yan, Z. 2006. The Weierstrass elliptic function
expansion method and its applications in nonlinear wave
equations. Chaos Soliton Fract, 29: 948-964.
- 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.
- 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.
- 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.
- Li, L., Li, E., Wang, M. 2010. The , G G Gl 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.
- Manafian, J. 2016. Optical soliton solutions for Schrödinger
type nonlinear evolution equations by the tan(Φ(ξ)/2)-
expansion method, Optik, 127: 4222-4245.
- Fan, E. 2000. Two new applications of the homogeneous
balance method, Phys. Let. A 265: 353–357.
- 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.
- Guo, P., Wu, X., Wang, L. 2015. Multiple soliton solutions
for the variant Boussinesq equations, Adv Differ Equ-Ny,
2015: 37.
- Khan, K., Akbar, MA. 2014. Study of analytical method
to seek for exact solutions of variant Boussinesq equations,
Springerplus, 3: 324.