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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 890784, 11 pages
http://dx.doi.org/10.1155/2013/890784
Research Article

A New Method with a Different Auxiliary Equation to Obtain Solitary Wave Solutions for Nonlinear Partial Differential Equations

Department of Mathematics, Firat University, 23119 Elazig, Turkey

Received 3 February 2013; Revised 22 April 2013; Accepted 23 April 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 Bülent Kiliç and Hasan Bulut. 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. B. R. Duffy and E. J. Parkes, “Travelling solitary wave solutions to a seventh-order generalized KdV equation,” Physics Letters A, vol. 214, no. 5-6, pp. 271–272, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  2. E. J. Parkes and B. R. Duffy, “Travelling solitary wave solutions to a compound KdV-Burgers equation,” Physics Letters A, vol. 229, no. 4, pp. 217–220, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. E. J. Parkes, “Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation,” Journal of Physics A, vol. 27, no. 13, pp. L497–L501, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhäuser, Boston, Mass, USA, 1997. View at Zentralblatt MATH · View at MathSciNet
  5. A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, The Netherlands, 2002.
  6. W. Hereman, P. P. Banerjee, A. Korpel, G. Assanto, A. van Immerzeele, and A. Meerpoel, “Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method,” Journal of Physics A, vol. 19, no. 5, pp. 607–628, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  7. X.-B. Hu and W.-X. Ma, “Application of Hirota's bilinear formalism to the Toeplitz lattice–-some special soliton-like solutions,” Physics Letters A, vol. 293, no. 3-4, pp. 161–165, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. M. Abourabia and M. M. El Horbaty, “On solitary wave solutions for the two-dimensional nonlinear modified Kortweg-de Vries-Burger equation,” Chaos, Solitons & Fractals, vol. 29, no. 2, pp. 354–364, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. L. Bock and M. D. Kruskal, “A two-parameter Miura transformation of the Benjamin-Ono equation,” Physics Letters A, vol. 74, no. 3-4, pp. 173–176, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer Series in Nonlinear Dynamics, Springer, Berlin, Germany, 1991. View at MathSciNet
  11. F. Cariello and M. Tabor, “Painlevé expansions for nonintegrable evolution equations,” Physica D, vol. 39, no. 1, pp. 77–94, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  12. E. Fan and H. Zhang, “New exact solutions to a solutions to a system of coupled KdV equations,” Physics Letters A, vol. 245, no. 5, pp. 389–392, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Fan, “Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations,” Physics Letters A, vol. 294, no. 1, pp. 26–30, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E.-G. Fan, “Traveling wave solutions for nonlinear equations using symbolic computation,” Computers & Mathematics with Applications, vol. 43, no. 6-7, pp. 671–680, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. Ugurlu and D. Kaya, “Solutions of the Cahn-Hilliard equation,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3038–3045, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. I. E. Inan, “Exact solutions to the various nonlinear evolution equations,” Physics Letters A, vol. 371, no. 1-2, pp. 90–95, 2007. View at Publisher · View at Google Scholar
  17. E. Fan and H. Zhang, “A note on homogeneous balance method,” Physics Letters A, vol. 246, no. 5, pp. 403–406, 1998. View at Publisher · View at Google Scholar
  18. L. Yang, Z. Zhu, and Y. Wang, “Exact solutions of nonlinear equations,” Physics Letters A, vol. 260, no. 1-2, pp. 55–59, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. Fan, “Two new applications of the homogeneous balance method,” Physics Letters A, vol. 265, no. 5-6, pp. 353–357, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,” Physics Letters A, vol. 199, no. 3-4, pp. 169–172, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. 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, no. 1–5, pp. 67–75, 1996. View at Publisher · View at Google Scholar
  22. B. Kiliç, Some methods for traveling wave solutions of the nonlinear partial differential equations and numerical analysis of these solutions [Ph.D. thesis], Firat University, 2012.