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Mathematical Problems in Engineering
Volume 2011, Article ID 810217, 23 pages
http://dx.doi.org/10.1155/2011/810217
Research Article

Trigonometric Function Periodic Wave Solutions and Their Limit Forms for the KdV-Like and the PC-Like Equations

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received 15 February 2011; Accepted 26 May 2011

Academic Editor: Ming Li

Copyright © 2011 Liu Zhengrong 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. B. Dey, “Domain wall solutions of KdV-like equations with higher order nonlinearity,” Journal of Physics A, vol. 19, no. 1, pp. L9–L12, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. B. Dey, “KdV like equations with domain wall solutions and their Hamiltonians,” in Solitons, pp. 188–194, Springer, Berlin, Germany, 1988. View at Google Scholar
  3. J. F. Zhang, “New solitary wave solution of the combined KdV and mKdV equation,” International Journal of Theoretical Physics, vol. 37, no. 5, pp. 1541–1546, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. J. F. Zhang, F. M. Wu, and J. Q. Shi, “Simple solition solution method for the combined KdV and mKdV equation,” International Journal of Theoretical Physics, vol. 39, no. 6, pp. 1697–1702, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. Yu, “Exact solitary wave solutions to a combined KdV and mKdV equation,” Mathematical Methods in the Applied Sciences, vol. 23, no. 18, pp. 1667–1670, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. R. Grimshaw, D. Pelinovsky, E. Pelinovsky, and A. Slunyaev, “Generation of large-amplitude solitons in the extended Korteweg-de Vries equation,” Chaos, vol. 12, no. 4, pp. 1070–1076, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. E. G. Fan, “Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method,” Journal of Physics A, vol. 35, no. 32, pp. 6853–6872, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. E. G. Fan, “Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics,” Chaos, Solitons and Fractals, vol. 16, no. 5, pp. 819–839, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. M. Y. Tang, R. Q. Wang, and Z. J. Jing, “Solitary waves and their bifurcations of KdV like equation with higher order nonlinearity,” Science in China A, vol. 45, no. 10, pp. 1255–1267, 2002. View at Google Scholar · View at Zentralblatt MATH
  10. Y.-Z. Peng, “New exact solutions to the combined KdV and mKdV equation,” International Journal of Theoretical Physics, vol. 42, no. 4, pp. 863–868, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. K. W. Chow, R. H. J. Grimshaw, and E. Ding, “Interactions of breathers and solitons in the extended Korteweg-de Vries equation,” Wave Motion, vol. 43, no. 2, pp. 158–166, 2005. View at Publisher · View at Google Scholar
  12. D. Kaya and I. E. Inan, “A numerical application of the decomposition method for the combined KdV—MKdV equation,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 915–926, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. E. Yomba, “The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations,” Physics Letters A, vol. 336, no. 6, pp. 463–476, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. W. G. Zhang and W. X. Ma, “Explicit solitary-wave solutions to generalized Pochhammer-Chree equations,” Applied Mathematics and Mechanics, vol. 20, no. 6, pp. 625–632, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J. B. Li and L. J. Zhang, “Bifurcations of traveling wave solutions in generalized Pochhammer-Chree equation,” Chaos, Solitons and Fractals, vol. 14, no. 4, pp. 581–593, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. D. Kaya, “The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation,” Physics Letters A, vol. 348, no. 3–6, pp. 244–250, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. Rafei, D. D. Ganji, H. R. M. Daniali, and H. Pashaei, “Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations,” Physics Letters A, vol. 364, no. 1, pp. 1–6, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. R. Liu, “Some new results on explicit traveling wave solutions of k(m,n) equation,” Discrete and Continuous Dynamical Systems B, vol. 13, no. 3, pp. 633–646, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. M. Li, S. C. Lim, and S. Y. Chen, “Exact solution of impulse response to a class of fractional oscillators and its stability,” Mathematical Problems in Engineering, vol. 2011, Article ID 657839, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. J.-B. Li, “Exact traveling wave solutions and dynamical behavior for the (n+1)-dimensional multiple sine-Gordon equation,” Science in China A, vol. 50, no. 2, pp. 153–164, 2007. View at Publisher · View at Google Scholar
  21. C. Cattani and G. Pierro, “Complexity on acute myeloid leukemia mRNA transcript variant,” Mathematical Problems in Engineering, vol. 2011, Article ID 379873, 16 pages, 2011. View at Publisher · View at Google Scholar
  22. C. Cattani and A. Kudreyko, “Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 570136, 8 pages, 2010. View at Publisher · View at Google Scholar
  23. Z. R. Liu and Z. Y. Ouyang, “A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations,” Physics Letters A, vol. 366, no. 4-5, pp. 377–381, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. E. G. Bakhoum and C. Toma, “Specific mathematical aspects of dynamics generated by coherence functions,” Mathematical Problems in Engineering, vol. 2011, Article ID 436198, 10 pages, 2011. View at Publisher · View at Google Scholar
  25. M.-Y. Tang and W.-L. Zhang, “Four types of bounded wave solutions of CH-γ equation,” Science in China A, vol. 50, no. 1, pp. 132–152, 2007. View at Publisher · View at Google Scholar
  26. Q.-D. Wang and M.-Y. Tang, “New explicit periodic wave solutions and their limits for modified form of Camassa-Holm equation,” Acta Mathematicae Applicatae Sinica, vol. 26, no. 3, pp. 513–524, 2010. View at Publisher · View at Google Scholar
  27. E. G. Bakhoum and C. Toma, “Mathematical transform of traveling-wave equations and phase aspects of quantum interaction,” Mathematical Problems in Engineering, vol. 2010, Article ID 695208, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. R. Liu, “Several new types of solitary wave solutions for the generalized Camassa-Holm-Degasperis-Procesi equation,” Communications on Pure and Applied Analysis, vol. 9, no. 1, pp. 77–90, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. S. Y. Chen, H. Tong, Z. Wang, S. Liu, M. Li, and B. Zhang, “Improved generalized belief propagation for vision processing,” Mathematical Problems in Engineering, vol. 2011, Article ID 416963, 12 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH