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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 178648, 4 pages
http://dx.doi.org/10.1155/2013/178648
Research Article

New Traveling Wave Solutions to the Vakhnenko-Parkes Equation

The School of Sciences, Guizhou Minzu University, Guiyang, Guizhou 550025, China

Received 12 June 2013; Accepted 29 July 2013

Academic Editors: G. Cleaver, J. Garecki, and D. Singleton

Copyright © 2013 XiaoHua Liu and Caixia He. 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. W.-X. Ma, T. Huang, and Y. Zhang, “A multiple exp-function method for nonlinear differential equations and its application,” Physica Scripta, vol. 82, no. 6, Article ID 065003, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. W.-X. Ma and E. Fan, “Linear superposition principle applying to Hirota bilinear equations,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 950–959, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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
  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, no. 1-5, pp. 67–75, 1996. View at Zentralblatt MATH · View at Scopus
  5. G. L. Lamb, Jr., “Bäcklund transformations for certain nonlinear evolution equations,” Journal of Mathematical Physics, vol. 15, pp. 2157–2165, 1974. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A.-M. Wazwaz, “New travelling wave solutions of different physical structures to generalized BBM equation,” Physics Letters A, vol. 355, no. 4-5, pp. 358–362, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. E. V. Krishnan, “On the Itô-type coupled nonlinear wave equation,” Journal of the Physical Society of Japan, vol. 55, no. 11, pp. 3753–3755, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Zhang, “A generalized new auxiliary equation method and its application to the (2+1)-dimensional breaking soliton equations,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 510–516, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  9. E. Yomba, “A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations,” Physics Letters A, vol. 372, no. 7, pp. 1048–1060, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Kangalgil and F. Ayaz, “New exact travelling wave solutions for the Ostrovsky equation,” Physics Letters A, vol. 372, no. 11, pp. 1831–1835, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. V. O. Vakhnenko and E. J. Parkes, “The two loop soliton solution of the Vakhnenko equation,” Nonlinearity, vol. 11, no. 6, pp. 1457–1464, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. A. Ostrovsky, “Nonlinear internal waves in a rotating ocean,” Oceanology, vol. 18, pp. 119–125, 1978.
  13. E. Yaşar, “New travelling wave solutions to the Ostrovsky equation,” Applied Mathematics and Computation, vol. 216, no. 11, pp. 3191–3194, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. Yusufoğlu and A. Bekir, “A travelling wave solution to the Ostrovsky equation,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 256–260, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. R. Abazari, “Application of (G'/G)-expansion method to travelling wave solutions of three nonlinear evolution equation,” Computers & Fluids, vol. 39, no. 10, pp. 1957–1963, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  16. X. Liu, W. Zhang, and Z. Li, “Application of improved (G'/G)-expansion method to traveling wave solutions of two nonlinear evolution equations,” Advances in Applied Mathematics and Mechanics, vol. 4, no. 1, pp. 122–130, 2012. View at MathSciNet