About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 284865, 7 pages
http://dx.doi.org/10.1155/2013/284865
Research Article

Abundant Exact Solition-Like Solutions to the Generalized Bretherton Equation with Arbitrary Constants

Department of Mathematics Sciences, Dezhou University, Dezhou 253023, China

Received 20 January 2013; Accepted 26 February 2013

Academic Editor: Abdel-Maksoud A. Soliman

Copyright © 2013 Xiuqing Yu 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. E. J. Parkes and B. R. Duffy, “An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations,” Computer Physics Communications, vol. 98, no. 3, pp. 288–300, 1996. View at Publisher · View at Google Scholar
  2. E. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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
  4. Z. Fu, S. Liu, S. Liu, and Q. Zhao, “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations,” Physics Letters A, vol. 290, no. 1-2, pp. 72–76, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Wang and Y. 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 · View at MathSciNet
  6. Y. Zhou, M. Wang, and T. Miao, “The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations,” Physics Letters A, vol. 323, no. 1-2, pp. 77–88, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Wang and X. Li, “Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations,” Physics Letters A, vol. 343, no. 1-3, pp. 48–54, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  8. 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
  9. A.-M. Wazwaz, “A study on nonlinear dispersive partial differential equations of compact and noncompact solutions,” Applied Mathematics and Computation, vol. 135, no. 2-3, pp. 399–409, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A.-M. Wazwaz, “A construction of compact and noncompact solutions for nonlinear dispersive equations of even order,” Applied Mathematics and Computation, vol. 135, no. 2-3, pp. 411–424, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. 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 MathSciNet
  12. M. Wang, “Exact solutions for a compound KdV-Burgers equation,” Physics Letters A, vol. 213, no. 5-6, pp. 279–287, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Wang, Y. Zhou, and Z. B. Li, “Application of a homogeneous balance method to exact solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 216, pp. 67–75, 1996. View at Publisher · View at Google Scholar
  14. C. Bai and H. Zhao, “New explicit exact solutions for the (2+1)-dimensional higher-order Broer-Kaup system,” Communications in Theoretical Physics, vol. 41, no. 4, pp. 521–526, 2004. View at MathSciNet
  15. L. Zhang, X. Liu, and C. Bai, “New multiple soliton-like and periodic solutions for (2+1)-dimensional canonical generalized KP equation with variable coefficients,” Communications in Theoretical Physics, vol. 46, pp. 793–798, 2006. View at Publisher · View at Google Scholar
  16. Sirendaoreji, “Auxiliary equation method and new solutions of Klein-Gordon equations,” Chaos, Solitons and Fractals, vol. 31, no. 4, pp. 943–950, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Sirendaoreji, “A new auxiliary equation and exact travelling wave solutions of nonlinear equations,” Physics Letters A, vol. 356, no. 2, pp. 124–130, 2006. View at Publisher · View at Google Scholar
  18. F. P. Bretherton, “Resonant interactions between waves. The case of discrete oscillations,” Journal of Fluid Mechanics, vol. 20, pp. 457–479, 1964. View at Publisher · View at Google Scholar · View at MathSciNet
  19. 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
  20. N. A. Kudryashov, D. I. Sinelshchikov, and M. V. Demina, “Exact solutions of the generalized Bretherton equation,” Physics Letters A, vol. 375, no. 7, pp. 1074–1079, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. N. G. Berloff and L. N. Howard, “Nonlinear wave interactions in nonlinear nonintegrable systems,” Studies in Applied Mathematics, vol. 100, no. 3, pp. 195–213, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. M. A. Akbar, H. Norhashidah, A. Mohd, and E. M. E. Zayed, “Abundant exact traveling wave solutions of generalized Bretherton equation via improved (G'/G)-expansion method,” Communications in Theoretical Physics, vol. 57, no. 2, pp. 173–178, 2012. View at Publisher · View at Google Scholar · View at MathSciNet