(G'/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation

Yıl 2010, Cilt: 7 Sayı: 1, - , 01.02.2010

İbrahim Enam İnan

Öz

In this study, we implemented the (G'/G)-expansion method the traveling
wave solutions of the sixth-order Ramani equation. By using this scheme, we found some
traveling wave solutions of the above-mentioned equation.

Anahtar Kelimeler

Sixth-order Ramani equation, traveling wave solutions, (G'/G)-expansion method

Kaynakça

• [1] L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
• [2] A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
• [3] X. B. Hu and W. X. Ma, Application of Hirota’s bilinear formalism to the Toeplitz lattice-some special soliton-like solutions, Phys. Lett. A 293 (2002), 161–165.
• [4] M. L. Wang and Y. M. Wang, A new B¨acklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients, Phys. Lett. A 287 (2001), 211–216.
• [5] A. M. Abourabia and M. M. El Horbaty, On solitary wave solutions for the two-dimensional nonlinear modified Kortweg-de Vries-Burger equation, Chaos, Solitons and Fractals 29 (2006), 354–364.
• [6] T. L. Bock and M. D. Kruskal, A two-parameter Miura transformation of the Benjamin-Ono equation, Phys. Lett. A 74 (1979), 173–176.
• [7] P. G. Drazin and R. S. Jhonson, Solitons: An Introduction, Cambridge University Press, Cambridge, 1989.
• [8] V. B. Matveev and M. A. Salle, Darboux transformations and solitons, Springer, Berlin, 1991.
• [9] F. Cariello and M. Tabor, Painlev´e expansions for nonintegrable evolution equations, Physica D 39 (1989), 77–94.
• [10] E. Fan, Two new applications of the homogeneous balance method, Phys. Lett. A 265 (2000), 353–357.
• [11] P. A. Clarkson, New Similarity Solutions for the Modified Boussinesq Equation, J. Phys. A: Math. Gen. 22 (1989), 2355–2367.
• [12] Y. Chuntao, A simple transformation for nonlinear waves, Phys. Lett. A 224 (1996), 77–84.
• [13] F. Zuntao, L. Shikuo, L. Shida and Z. Qiang, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A 290 (2001), 72–76.
• [14] J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals 30 (2006), 700–708.
• [15] W. Hereman, A. Korpel and P. P. Banerjee, Wave Motion 7 (1985), 283–289.
• [16] W. Hereman and M. Takaoka, Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA, J. Phys. A: Math. Gen. 23 (1990), 4805–4822.
• [17] H. Lan and K. Wang, Exact solutions for two nonlinear equations, J. Phys. A: Math. Gen. 23 (1990), 3923–3928.
• [18] S. Lou, G. Huang and H. Ruan, Exact solutions for two nonlinear equations, J. Phys. A: Math. Gen. 24 (1991), L587–L590.
• [19] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60 (1992), 650–654.
• [20] E. J. Parkes and B. R. Duffy, An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commun. 98 (1996), 288–300.
• [21] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000), 212–218.
• [22] S. A. Elwakil, S. K. El-labany, M. A. Zahran, and R. Sabry, Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Lett. A 299 (2002), 179–188.
• [23] X. Zheng, Y. Chen, and H. Zhang, Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation, Phys. Lett. A 311 (2003), 145–157.
• [24] E. Yomba, Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation, Chaos, Solitons & Fractals 20 (2004), 1135–1139.
• [25] H. Chen and H. Zhang, New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation, Chaos, Solitons & Fractals 19 (2004), 71–76.
• [26] M. Wang, J. Zhang and X. Li Application of the (G0/G)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations, Appl. Math. and Comput. 206 (2008), 321–326.