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

Year 2010, Volume: 7 Issue: 1, - , 01.02.2010

Abstract

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.

References

  • [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.
Year 2010, Volume: 7 Issue: 1, - , 01.02.2010

Abstract

References

  • [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.
There are 26 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

İbrahim Enam İnan

Publication Date February 1, 2010
Published in Issue Year 2010 Volume: 7 Issue: 1

Cite

APA İnan, İ. E. (2010). (G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation. Cankaya University Journal of Science and Engineering, 7(1).
AMA İnan İE. (G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation. CUJSE. February 2010;7(1).
Chicago İnan, İbrahim Enam. “(G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation”. Cankaya University Journal of Science and Engineering 7, no. 1 (February 2010).
EndNote İnan İE (February 1, 2010) (G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation. Cankaya University Journal of Science and Engineering 7 1
IEEE İ. E. İnan, “(G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation”, CUJSE, vol. 7, no. 1, 2010.
ISNAD İnan, İbrahim Enam. “(G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation”. Cankaya University Journal of Science and Engineering 7/1 (February 2010).
JAMA İnan İE. (G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation. CUJSE. 2010;7.
MLA İnan, İbrahim Enam. “(G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation”. Cankaya University Journal of Science and Engineering, vol. 7, no. 1, 2010.
Vancouver İnan İE. (G’/G)-Expansion Method for Traveling Wave Solutions of the Sixth-Order Ramani Equation. CUJSE. 2010;7(1).