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International Journal of Differential Equations
Volume 2010 (2010), Article ID 954674, 11 pages
http://dx.doi.org/10.1155/2010/954674
Research Article

Solitary Wave Solutions for a Time-Fraction Generalized Hirota-Satsuma Coupled KdV Equation by a New Analytical Technique

Department of Mechanical Engineering, Babol University of Technology, P. O. Box 484, 47148 71167 Babol, Iran

Received 17 May 2009; Accepted 7 July 2009

Academic Editor: Shaher Momani

Copyright © 2010 Majid Shateri and D. D. Ganji. 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. I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.
  2. F. Mainardi, Fractional Calculus Some Basic Problems in Continuum and Statistical Mechanics, Springer, New York, NY, USA, 1997.
  3. W. R. Schneider and W. Wyss, “Fractional diffusion and wave equations,” Journal of Mathematical Physics, vol. 30, pp. 134–144, 1989.
  4. J. H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, pp. 57–68, 1998.
  5. J. H. He, “Variational iteration method—some recent results and new interpretations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 3–17, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. H. He and X. H. Wu, “Variational iteration method: new development and applications,” Computers and Mathematics with Applications, vol. 54, no. 7-8, pp. 881–894, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. Tari, D. D. Ganji, and H. Babazadeh, “The application of He's variational iteration method to nonlinear equations arising in heat transfer,” Physics Letters, Section A, vol. 363, no. 3, pp. 213–217, 2007. View at Publisher · View at Google Scholar
  8. S. Abbasbandy and A. Shirzadi, “The variational iteration method for a family of fifth-order boundary value differential equations,” International Journal of Nonlinear Dynamics in Engineering and Sciences, vol. 1, no. 1, pp. 39–46, 2009.
  9. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, Mass, USA, 1994.
  10. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988.
  11. G. Adomian, “Solutions of nonlinear P.D.E,” Applied Mathematics Letters, vol. 11, no. 3, pp. 121–123, 1998.
  12. Q. Esmaili, A. Ramiar, E. Alizadeh, and D. D. Ganji, “An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method,” Physics Letters A, vol. 372, no. 19, pp. 3434–3439, 2008. View at Publisher · View at Google Scholar
  13. A. M. Wazwaz, “A new algorithm for calculating adomian polynomials for nonlinear operators,” Applied Mathematics and Computation, vol. 111, no. 1, pp. 53–69, 2000.
  14. S. Momani and Z. Odibat, “Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 177, pp. 488–494, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. R. Hirota and J. Satsuma, “Soliton solutions of a coupled Korteweg-de Vries equation,” Physics Letters A, vol. 85, no. 8-9, pp. 407–408, 1981.
  16. Y. Wu, X. Geng, X. Hu, and S. Zhu, “A generalized Hirota-Satsuma coupled Korteweg-de vries equation and Miura transformations,” Physics Letters A, vol. 255, pp. 259–264, 1999.
  17. I. Podlubny, “Numerical solution of ordinary fractional differential equations by the fractional difference method,” in Advances in Difference Equations, S. Elaydi, I. Gyori, and G. Ladas, Eds., Gordon and Breach, Amsterdam, The Netherlands, 1997.
  18. M. Caputo, “Linear models of dissipation whose Q is almost frequency independent,” Journal of the Royal Astronomical Society, vol. 13, pp. 529–539, 1967.
  19. A. Ghorbani, “Toward a new analytical method for solving nonlinear fractional differential equations,” Computer Methods in Applied Mechanics and Engineering, vol. 197, pp. 4173–4179, 2008. View at Publisher · View at Google Scholar
  20. M. Reed and B. Simon, Methods of Modern Mathematical Physics, I: Functional Analysis, Academic Press, New York, NY, USA, 1980.
  21. Z. Z. Ganji, D. D. Ganji, and Y. Rostamiyan, “Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 3107–3113, 2009. View at Publisher · View at Google Scholar · View at MathSciNet