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Journal of Applied Mathematics
Volume 2014, Article ID 384969, 6 pages
http://dx.doi.org/10.1155/2014/384969
Research Article

The -Expansion Method and Its Application for Higher-Order Equations of KdV (III)

College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 17 September 2013; Revised 23 December 2013; Accepted 16 January 2014; Published 20 February 2014

Academic Editor: Alberto Cabada

Copyright © 2014 Huizhang Yang 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. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, UK, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  2. C. Rogers and W. F. Shadwick, Backlund Transformations, Academic Press, New York, NY, USA, 1982.
  3. Q.-X. Qu, B. Tian, K. Sun, and Y. Jiang, “Bäcklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation,” Journal of Mathematical Physics, vol. 52, no. 1, Article ID 013511, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  4. C. H. Gu, H. S. Hu, and Z. X. Zhou, Darboux Transformations in Integrable Systems Theory and their Applications to Geometry, vol. 26 of Mathematical Physics Studies, Springer, Dordrecht, The Netherlands, 2005. View at MathSciNet
  5. R. Hirota, “Exact solution of the Korteweg-de Vries equation formultiple Collisions of solitons,” Physical Review Letters, vol. 27, no. 18, pp. 1192–1194, 1971. View at Google Scholar
  6. X.-H. Wu and J.-H. He, “EXP-function method and its application to nonlinear equations,” Chaos, Solitons & Fractals, vol. 38, no. 3, pp. 903–910, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Zhang, “Application of Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations,” Physics Letters A, vol. 372, no. 11, pp. 1873–1880, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. A. Abdou, “The extended tanh method and its applications for solving nonlinear physical models,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 988–996, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. N. A. Kudryashov, “Exact solutions of the generalized Kuramoto-Sivashinsky equation,” Physics Letters A, vol. 147, no. 5-6, pp. 287–291, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. Liu, Z. Fu, S. Liu, and Q. Zhao, “Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations,” Physics Letters A, vol. 289, no. 1-2, pp. 69–74, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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 MathSciNet
  13. A. Malik, F. Chand, and S. C. Mishra, “Exact travelling wave solutions of some nonlinear equations by G/G-expansion method,” Applied Mathematics and Computation, vol. 216, no. 9, pp. 2596–2612, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. A. Bekir, “Application of the G/G-expansion method for nonlinear evolution equations,” Physics Letters A, vol. 372, no. 19, pp. 3400–3406, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  15. E. M. E. Zayed, “New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G/G)-expansion method,” Journal of Applied Mathematics & Informatics, vol. 28, no. 1-2, pp. 383–395, 2010. View at Google Scholar
  16. H. Naher, F. A. Abdullah, and M. Ali Akbar, “The G/G-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation,” Mathematical Problems in Engineering, vol. 2011, Article ID 218216, 11 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  17. E. M. E. Zayed, “New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized G/G-expansion method,” Journal of Physics. A. Mathematical and Theoretical, vol. 42, no. 19, Article ID 195202, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Y.-B. Zhou and C. Li, “Application of modified G/G-expansion method to traveling wave solutions for Whitham-Broer-Kaup-like equations,” Communications in Theoretical Physics, vol. 51, no. 4, pp. 664–670, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  19. 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
  20. S. Guo, Y. Zhou, and C. Zhao, “The improved G/G-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations,” Applied Mathematics and Computation, vol. 216, no. 7, pp. 1965–1971, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. A. Akbar, N. H. Ali, and E. M. E. Zayed, “A generalized and improved (G/G)-expansion method for nonlinear evolution equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 459879, 22 pages, 2012. View at Publisher · View at Google Scholar
  22. L.-X. Li, E.-Q. Li, and M.-L. 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 · View at MathSciNet
  23. A. S. Fokas, “On a class of physically important integrable equations,” Physica D, vol. 87, no. 1–4, pp. 145–150, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. B. Li, W. Rui, Y. Long, and B. He, “Travelling wave solutions for higher-order wave equations of KdV type III,” Mathematical Biosciences and Engineering, vol. 3, no. 1, pp. 125–135, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. W. Rui, Y. Long, and B. He, “Some new travelling wave solutions with singular or nonsingular character for the higher order wave equation of KdV type (III),” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 11, pp. 3816–3828, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. W. Rui, Y. Long, and B. He, “Periodic wave solutions and solitary cusp wave solutions for a higher order wave equation of KdV type,” Rostocker Mathematisches Kolloquium, vol. 61, pp. 57–71, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet