About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 892420, 10 pages
http://dx.doi.org/10.1155/2012/892420
Research Article

New Exact Solutions to the KdV-Burgers-Kuramoto Equation with the Exp-Function Method

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

Received 9 February 2012; Accepted 19 March 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 Jae-Myoung Kim and Changbum Chun. 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. J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. S. D. Zhu, “Exp-function method for the Hybrid-Lattice system,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 461–464, 2007. View at Scopus
  3. S. D. Zhu, “Exp-function method for the discrete mKdV lattice,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 465–468, 2007. View at Scopus
  4. S. Zhang, “Explicit and exact nontravelling wave solutions of Konopelchenko-Dubrovsky equations,” Zeitschrift fur Naturforschung A, vol. 62, no. 12, pp. 689–697, 2007. View at Scopus
  5. S. Zhang, “Application of Exp-function method to a KdV equation with variable coefficients,” Physics Letters A, vol. 365, no. 5-6, pp. 448–453, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. Zhang, “Exp-function method: solitary, periodic and rational wave solutions of nonlinear evolution equations,” Nonlinear Science Letters A, vol. 1, no. 2, pp. 143–146, 2010.
  7. A. Bekir and A. Boz, “Exact solutions for a class of nonlinear partial differential equations using exp-function method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 4, pp. 505–512, 2007. View at Scopus
  8. J. H. He, “An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering,” International Journal of Modern Physics B, vol. 22, no. 21, pp. 3487–3578, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. X. W. Zhou, Y. X. Wen, and J. H. He, “Exp-function method to solve the nonlinear dispersive K(m,n) equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 3, pp. 301–306, 2008. View at Scopus
  10. C. Q. Dai and Y. Y. Wang, “Exact travelling wave solutions of toda lattice equations obtained via the exp-function method,” Zeitschrift fur Naturforschung A, vol. 63, no. 10-11, pp. 657–662, 2008. View at Scopus
  11. A. Bekir and A. Boz, “Exact solutions for nonlinear evolution equations using Exp-function method,” Physics Letters A, vol. 372, no. 10, pp. 1619–1625, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. C. Chun, “Solitons and periodic solutions for the fifth-order KdV equation with the Exp-function method,” Physics Letters A, vol. 372, no. 16, pp. 2760–2766, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J.-H. He and L.-N. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method,” Physics Letters A, vol. 372, no. 7, pp. 1044–1047, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. Ebaid, “Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method,” Physics Letters A, vol. 365, no. 3, pp. 213–219, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. M. A. Noor, K. I. Noor, A. Waheed, and E. A. Al-Said, “Some new solitonary solutions of the modified Benjamin-Bona-Mahony equation,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 2126–2131, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. E. M. E. Zayed and M. A. M. Abdelaziz, “Exact solutions for the nonlinear Schrödinger equation with variable coefficients using the generalized extended tanh-function, the sine-cosine and the exp-function methods,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 2259–2268, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. K. Parand and J. A. Rad, “Exp-function method for some nonlinear PDE's and a nonlinear ODE's,” Journal of King Saud University, vol. 24, no. 1, pp. 1–10, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Kuramoto and T. Tsuzuki, “Persistent propagation of concentration waves in dissipative media far from thermal equilibrium,” Progress of Theoretical Physics, vol. 55, no. 2, pp. 356–369, 1967.
  19. T. Kawahara and M. Tanaka, “Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation,” Physics Letters A, vol. 97, no. 8, pp. 311–314, 1983. View at Publisher · View at Google Scholar
  20. S. Zhang, “New exact solutions of the KdV-Burgers-Kuramoto equation,” Physics Letters A, vol. 358, no. 5-6, pp. 414–420, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. E. Yusufoğlu and A. Bekir, “The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations,” Chaos, Solitons & Fractals, vol. 38, no. 4, pp. 1126–1133, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. E. Fan and H. Zhang, “A note on the homogeneous balance method,” Physics Letters A, vol. 246, no. 5, pp. 403–406, 1998. View at Scopus
  23. H. B. Lan and K. L. Wang, “Exact solutions for two nonlinear equations. I,” Journal of Physics A, vol. 23, no. 17, pp. 3923–3928, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. L. Yang and K. Q. Yang, “Solitary wave solutions of generalized Kuramoto-Sivashinsky equations,” Journal of Lanzhou University, vol. 34, no. 4, pp. 53–55, 1998 (Chinese).
  25. J. Weiss, M. Tabor, and G. Carnevale, “The Painlevé property for partial differential equations,” Journal of Mathematical Physics, vol. 24, no. 3, pp. 522–526, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. P. A. Clarkson and E. L. Mansfield, “On a shallow water wave equation,” Nonlinearity, vol. 7, no. 3, pp. 975–1000, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH