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Mathematical Problems in Engineering
Volume 2013, Article ID 128970, 8 pages
http://dx.doi.org/10.1155/2013/128970
Research Article

New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using Extended F-Expansion Method

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

Received 23 September 2013; Accepted 4 December 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Yinghui He 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, New York, NY, USA, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  2. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin, Germany, 1991. View at MathSciNet
  3. R. Hirota, “Exact solutions of the Korteweg-de Vries eauation for multiple collisions of solutions,” Physical Review Letters, vol. 27, pp. 1192–1194, 1971. View at Google Scholar
  4. M. Wang, Y. Zhou, and Z. Li, “Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics,” Physics Letters A, vol. 216, pp. 67–75, 1996. View at Google Scholar
  5. 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
  6. E. J. Parkes and B. R. Duffy, “An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations,” Computer Physics Communications, vol. 98, pp. 288–300, 1996. View at Google Scholar
  7. J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. J. Mohamad Jawad, M. D. Petković, and A. Biswas, “Modified simple equation method for nonlinear evolution equations,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 869–877, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. E. Fan, “Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics,” Chaos, Solitons and Fractals, vol. 16, no. 5, pp. 819–839, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Wang and X. Li, “Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1257–1268, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  11. D. Wang and H.-Q. Zhang, “Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation,” Chaos, Solitons and Fractals, vol. 25, no. 3, pp. 601–610, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  12. E. Yomba, “The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations,” Physics Letters A, vol. 336, no. 6, pp. 463–476, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. 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
  14. N. A. Kudryashov, “On types of nonlinear nonintegrable equations with exact solutions,” Physics Letters A, vol. 155, no. 4-5, pp. 269–275, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  15. N. A. Kudryashov, “Exact solitary waves of the Fisher equation,” Physics Letters A, vol. 342, no. 1-2, pp. 99–106, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. N. A. Kudryashov, “Simplest equation method to look for exact solutions of nonlinear differential equations,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1217–1231, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. 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
  18. E. Tzirtzilakis, V. Marinakis, C. Apokis, and T. Bountis, “Soliton-like solutions of higher order wave equations of the Korteweg-de Vries type,” Journal of Mathematical Physics, vol. 43, no. 12, pp. 6151–6165, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. Tzirtzilakis, M. Xenos, V. Marinakis, and T. C. Bountis, “Interactions and stability of solitary waves in shallow water,” Chaos, Solitons & Fractals, vol. 14, no. 1, pp. 87–95, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. B. Fuchssteiner and A. S. Fokas, “Symplectic structures, their Bäcklund transformations and hereditary symmetries,” Physica D, vol. 4, no. 1, pp. 47–66, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  21. R. Camassa and D. D. Holm, “An integrable shallow water equation with peaked solitons,” Physical Review Letters, vol. 71, no. 11, pp. 1661–1664, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. Y. Kodama and A. V. Mikhailov, “Obstacles to asymptotic integrability,” in Algebraic Aspects of Integrable Systems, I. M. Gelfand and A. Fokas, Eds., Birkhäuser, Boston, Mass, USA, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. X. Wu, W. Rui, and X. Hong, “A generalized KdV equation of neglecting the highest-order infinitesimal term and its exact traveling wave solutions,” Abstract and Applied Analysis, vol. 2013, Article ID 656297, 15 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet