Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 183159, 14 pages
http://dx.doi.org/10.1155/2013/183159
Research Article

Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation

1College of Mathematics, Honghe University, Mengzi, Yunnan 661100, China
2Department of Physics, Honghe University, Mengzi, Yunnan 661100, China

Received 27 May 2013; Revised 26 July 2013; Accepted 26 July 2013

Academic Editor: Jingxin Zhang

Copyright © 2013 Bin He 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. M. Chen, S. Q. Liu, and Y. Zhang, “A two-component generalization of the Camassa-Holm equation and its solutions,” Letters in Mathematical Physics, vol. 75, no. 1, pp. 1–15, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. Camassa and D. D. Holm, “An integrable shallow water equation with peaked solitons,” Physical Review Letters, vol. 71, no. 11, pp. 1661–1664, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Y. Fu and C. Z. Qu, “Well posedness and blow-up solution for a new coupled Camassa-Holm equations with peakons,” Journal of Mathematical Physics, vol. 50, no. 1, Article ID 012906, pp. 1–24, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. B. Jin and Z. G. Guo, “On a two-component Degasperis-Procesi shallow water system,” Nonlinear Analysis. Real World Applications, vol. 11, no. 5, pp. 4164–4173, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Yuen, “Self-similar blowup solutions to the 2-component Degasperis-Procesi shallow water system,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3463–3469, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. Degasperis and M. Procesi, “Asymptotic integrability,” in Symmetry and Perturbation Theory, pp. 23–37, World Scientific, Singapore, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. B. Li and H. H. Dai, On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach, Science Press, Beijing, China, 2007.
  8. J. B. Li and Y. S. Li, “Bifurcations of travelling wave solutions for a two-component Camassa-Holm equation,” Acta Mathematica Sinica, vol. 24, no. 8, pp. 1319–1330, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. B. He, “Bifurcations and exact bounded travelling wave solutions for a partial differential equation,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 364–371, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Li and Z. Liu, “Smooth and non-smooth traveling waves in a nonlinearly dispersive equation,” Applied Mathematical Modelling, vol. 25, no. 1, pp. 41–56, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Springer, Berlin, Germany, 1971. View at MathSciNet