About this Journal Submit a Manuscript Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 854619, 16 pages
http://dx.doi.org/10.1155/2012/854619
Research Article

New Jacobi Elliptic Function Solutions for the Zakharov Equations

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

Received 4 September 2012; Revised 22 October 2012; Accepted 23 October 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 Yun-Mei Zhao. 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. L. Wang and Y. B. Zhou, “The periodic wave solutions for the Klein-Gordon-Schrödinger equations,” Physics Letters A, vol. 318, no. 1-2, pp. 84–92, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. Z. Yan and H. Zhang, “New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water,” Physics Letters A, vol. 285, no. 5-6, pp. 355–362, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. M. L. Wang, Y. B. Zhou, and Z. B. 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.
  4. 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
  5. Y. L. Ma, B. Q. Li, and C. Wang, “A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method,” Applied Mathematics and Computation, vol. 211, no. 1, pp. 102–107, 2009. View at Publisher · View at Google Scholar
  6. 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
  7. H. Bin, M. Qing, L. Yao, and R. Weiguo, “New exact solutions of the double sine-Gordon equation using symbolic computations,” Applied Mathematics and Computation, vol. 186, no. 2, pp. 1334–1346, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. M. L. Wang, X. Z. Li, and J. L. Zhang, “The (G/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008. View at Publisher · View at Google Scholar
  9. E. M. E. Zayed, “New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G/G)-expansion method,” Journal of Physics A, vol. 42, no. 19, Article ID 195202, p. 13, 2009. View at Publisher · View at Google Scholar
  10. Y.-B. Zhou and C. Li, “Application of modified (G/G)-expansion method to traveling wave solutions for Whitham-Broer-Kaup-like equations,” Communications in Theoretical Physics, vol. 51, no. 4, pp. 664–670, 2009. View at Publisher · View at Google Scholar
  11. S. M. Guo and Y. B. Zhou, “The extended (G/G)-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations,” Applied Mathematics and Computation, vol. 215, no. 9, pp. 3214–3221, 2010. View at Publisher · View at Google Scholar
  12. S. M. Guo, Y. B. Zhou, and C. X. Zhao, “The improved (G/G)-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations,” Applied Mathematics and Computation, vol. 216, no. 7, pp. 1965–1971, 2010. View at Publisher · View at Google Scholar
  13. L. X. Li, E. Q. Li, and M. L. Wang, “The (G'/G,1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations,” Applied Mathematics, vol. 25, no. 4, pp. 454–462, 2010. View at Publisher · View at Google Scholar
  14. D. J. Huang and H. Q. Zhang, “Extended hyperbolic function method and new exact solitary wave solutions of Zakharov equations,” Acta Physica Sinica, vol. 53, no. 8, pp. 2434–2438, 2004. View at Zentralblatt MATH
  15. S. D. Liu, Z. T. Fu, S. K. Liu, and Q. Zhang, “The envelope periodic solutions to nonlinearwave equations with Jacobi elliptic function,” Acta Physica Sinica, vol. 51, pp. 718–722, 2002.
  16. Y. D. Shang, Y. Huang, and W. J. Yuan, “The extended hyperbolic functions method and new exact solutions to the Zakharov equations,” Applied Mathematics and Computation, vol. 200, no. 1, pp. 110–122, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. L. Wang, Y. M. Wang, and J. L. Zhang, “The periodic wave solutions for two systemsof nonlinear wave equations,” Chinese Physics, vol. 12, pp. 1341–1348, 2003.
  18. C. H. Zhao and Z. M. Sheng, “Explicit travelling wave solutions for Zakharov equations,” Acta Physica Sinica, vol. 53, no. 6, pp. 1629–1634, 2004. View at Zentralblatt MATH
  19. J. L. Zhang, Y. M. Wang, and M. L. Wang, “Exact solutions to two nonlinear equations,” Acta Physica Sinica, vol. 52, no. 7, pp. 1574–1578, 2003. View at Zentralblatt MATH
  20. A. Ebaid and E. H. Aly, “Exact solutions for the transformed reduced Ostrovsky equation via the F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions,” Wave Motion, vol. 49, no. 2, pp. 296–308, 2012. View at Publisher · View at Google Scholar