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Mathematical Problems in Engineering
Volume 2011, Article ID 218216, 11 pages
http://dx.doi.org/10.1155/2011/218216
Research Article

The ( 𝐺 / 𝐺 ) -Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 24 June 2011; Accepted 22 September 2011

Academic Editor: Kue-Hong Chen

Copyright © 2011 Hasibun Naher et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Jianming, D. Jie, and Y. Wenjun, “Backlund transformation and new exact solutions of the Sharma-Tasso-Olver equation,” Abstract and Applied Analysis, Article ID 935710, 8 pages, 2011. View at Google Scholar · View at Zentralblatt MATH
  2. K. Al-Khaled, M. Al-Refai, and A. Alawneh, “Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations,” Applied Mathematics and Computation, vol. 202, no. 1, pp. 233–242, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. A. Bekir, “Applications of the extended tanh method for coupled nonlinear evolution equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 9, pp. 1748–1757, 2008. View at Publisher · View at Google Scholar
  4. S. A. Yousefi, A. Lotfi, and M. Dehghan, “He's variational iteration method for solving nonlinear mixed volterra-fredholm integral equations,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2172–2176, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. Rajaram and M. Najafi, “Analytical treatment and convergence of the adomian decomposition method for a system of coupled damped wave equations,” Applied Mathematics and Computation, vol. 212, no. 1, pp. 72–81, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. L. Li, “Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 168–173, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. Hesameddini and A. Peyrovi, “Homotopy perturbation method for second painleve equation and comparisons with analytic continuation extension and chebishev series method,” Journal for Theory and Applications, vol. 5, no. 13, pp. 629–637, 2010. View at Google Scholar
  8. E. S. A. Alaidarous, “F-expansion method for the nonlinear generalized Ito system,” International Journal of Basic & Applied Sciences, vol. 10, no. 2, pp. 90–117, 2010. View at Google Scholar
  9. Z. J. Zhou, J. Z. Fu, and Z. B. Li, “Maple packages for computing Hirota's bilinear equation and multisoliton solutions of nonlinear evolution equations,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 92–104, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Bekir and E. Aksoy, “Exact solutions of nonlinear evolution equations with variable coefficients using exp-function method,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 430–436, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. A. H. Salas and C. A. Gomez, “Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation,” Mathematical Problems in Engineering, Article ID 194329, 14 pages, 2010. View at Google Scholar · View at Zentralblatt MATH
  12. A. H. Salas and C. A. Gomez, “Exact solutions for a third-order KdV equation with variable coefficients and forcing term,” Mathematical Problems in Engineering, Article ID 737928, 13 pages, 2009. View at Google Scholar · View at Zentralblatt MATH
  13. M. A. Noor and S. T. Mohyud-Din, “Modified variational iteration method for goursat and laplace problems,” World Applied Sciences Journal, vol. 4, no. 4, pp. 487–498, 2008. View at Google Scholar
  14. W. X. Ma and J. H. Lee, “A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1356–1363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Y. Khan, N. Faraz, and A. Yildirim, “New soliton solutions of the generalized Zakharov equations using he's variational approach,” Applied Mathematics Letters, vol. 24, no. 6, pp. 965–968, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. A. El-Wakil, A. R. Degheidy, E. M. Abulwafa, M. A. Madkour, M. T. Attia, and M. A. Abdou, “Exact travelling wave solutions of generalized Zakharov equations with arbitrary power nonlinearities,” International Journal of Nonlinear Science, vol. 7, no. 4, pp. 455–461, 2009. View at Google Scholar
  17. S. M. Sayed, O. O. Elhamahmy, and G. M. Gharib, “Travelling wave solutions for the KdV-Burgers-Kuramoto and nonlinear Schrodinger equations which describe pseudospherical surfaces,” Journal of Applied Mathematics, Article ID 576783, 10 pages, 2008. View at Google Scholar · View at Zentralblatt MATH
  18. J. Zhou, L. Tian, and X. Fan, “Soliton and periodic wave solutions to the osmosis (2, 2) equation,” Mathematical Problems in Engineering, Article ID 509390, 10 pages, 2009. View at Google Scholar · View at Zentralblatt MATH
  19. M. A. Noor, K. I. Noor, E. Al-Said, and M. Waseem, “Some new iterative methods for nonlinear equations,” Mathematical Problems in Engineering, Article ID 198943, 12 pages, 2010. View at Google Scholar · View at Zentralblatt MATH
  20. C. A. Gomez and A. H. Salas, “Exact solutions for the generalized BBM equation with variable coefficients,” Mathematical Problems in Engineering, Article ID 498249, 10 pages, 2010. View at Google Scholar · View at Zentralblatt MATH
  21. M. Wang, X. Li, and J. Zhang, “The (G/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. R. Abazari, “Application of (G/G)-expansion method to travelling wave solutions of three nonlinear evolution equation,” Computers & Fluids, vol. 39, no. 10, pp. 1957–1963, 2010. View at Publisher · View at Google Scholar
  23. B. Zheng, “Travelling wave solutions of two nonlinear evolution equations by using the (G/G)-expansion method,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5743–5753, 2011. View at Publisher · View at Google Scholar
  24. J. Feng, W. Li, and Q. Wan, “Using (G/G)-expansion method to seek the traveling wave solution of Kolmogorov-Petrovskii-Piskunov equation,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5860–5865, 2011. View at Publisher · View at Google Scholar
  25. X. Liu, L. Tian, and Y. Wu, “Application of (G/G)-expansion method to two nonlinear evolution equations,” Applied Mathematics and Computation, vol. 217, no. 4, pp. 1376–1384, 2010. View at Publisher · View at Google Scholar
  26. J. Feng, “New traveling wave solutions to the seventh-order Sawada-Kotera equation,” Journal of Applied Mathematics & Informatics, vol. 28, no. 5-6, pp. 1431–1437, 2010. View at Google Scholar
  27. S. Guo and Y. Zhou, “The extended (G/G)-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations,” Applied Mathematics and Computation, vol. 215, no. 9, pp. 3214–3221, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  28. E. M. E. Zayed and S. Al-Joudi, “Applications of an extended (G/G)-expansion method to find exact solutions of nonlinear PDEs in mathematical physics,” Mathematical Problems in Engineering, vol. 2010, Article ID 768573, 19 pages, 2010. View at Google Scholar
  29. J. Zhang, F. Jiang, and X. Zhao, “An improved (G/G)-expansion method for solving nonlinear evolution equations,” International Journal of Computer Mathematics, vol. 87, no. 8, pp. 1716–1725, 2010. View at Publisher · View at Google Scholar
  30. L. Li, E. Li, and M. Wang, “The (G/G,1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations,” Applied Mathematics B, vol. 25, no. 4, pp. 454–462, 2010. View at Publisher · View at Google Scholar
  31. M. Hayek, “Constructing of exact solutions to the KdV and Burgers equations with power-law nonlinearity by the extended (G/G)-expansion method,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 212–221, 2010. View at Publisher · View at Google Scholar
  32. L. Jin, “Application of the variational iteration method for solving the fifth order caudrey-dodd-gibbon equation,” International Mathematical Forum, vol. 5, no. 66, pp. 3259–3265, 2010. View at Google Scholar · View at Zentralblatt MATH
  33. A. Salas, “Some exact solutions for the caudrey-dodd-gibbon equation,” Mathematical Physics, 2008, arXiv:0805.2969v2. View at Google Scholar
  34. A. M. Wazwaz, “Analytic study of the fifth order integrable nonlinear evolution equations by using the tanh method,” Applied Mathematics and Computation, vol. 174, no. 1, pp. 289–299, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet