Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 109235, 14 pages
http://dx.doi.org/10.1155/2012/109235
Research Article

Kink Waves and Their Evolution of the RLW-Burgers Equation

1School of Mathematics, Chengdu University of Information Technology, Sichuan, Chengdu 610225, China
2School of Computer Science Technology, Southwest University for Nationalities, Sichuan, Chengdu 610041, China

Received 13 March 2012; Revised 26 May 2012; Accepted 11 June 2012

Academic Editor: Victor M. Perez Garcia

Copyright © 2012 Yuqian Zhou and Qian Liu. 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. J. L. Bona, W. G. Pritchard, and L. R. Scott, “An evaluation of a model equation for water waves,” Philosophical Transactions of the Royal Society of London A, vol. 302, no. 1471, pp. 457–510, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. D. H. Peregrine, “Calculations of the development of an unduiar bore,” Journal of Fluid Mechanics, vol. 25, pp. 321–330, 1966. View at Publisher · View at Google Scholar
  3. C. J. Amick, J. L. Bona, and M. E. Schonbek, “Decay of solutions of some nonlinear wave equations,” Journal of Differential Equations, vol. 81, no. 1, pp. 1–49, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. W. G. Zhang and M. L. Wang, “A class of exact travelling wave solutions to the B-BBM equation and their structure,” Acta Mathematica Scientia A, vol. 12, no. 3, pp. 325–331, 1992. View at Google Scholar
  5. M. L. Wang, “Exact solutions for the RLW-Burgers equation,” Mathematica Applicata, vol. 8, no. 1, pp. 51–55, 1995. View at Google Scholar · View at Zentralblatt MATH
  6. B. Katzengruber, M. Krupa, and P. Szmolyan, “Bifurcation of traveling waves in extrinsic semiconductors,” Physica D, vol. 144, no. 1-2, pp. 1–19, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. B. Li and H. H. Dai, On the Study of Singular Nonlinear Traveling Wave Equation: Dynamical System Approach, Science Press, Beijing, China, 2007.
  8. D. Peterhof, B. Sandstede, and A. Scheel, “Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders,” Journal of Differential Equations, vol. 140, no. 2, pp. 266–308, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. F. Sánchez-Garduño and P. K. Maini, “Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations,” Journal of Mathematical Biology, vol. 35, no. 6, pp. 713–728, 1997. View at Publisher · View at Google Scholar
  10. A. Constantin and W. Strauss, “Exact periodic traveling water waves with vorticity,” Comptes Rendus Mathématique, vol. 335, no. 10, pp. 797–800, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J. Huang, G. Lu, and S. Ruan, “Existence of traveling wave solutions in a diffusive predator-prey model,” Journal of Mathematical Biology, vol. 46, no. 2, pp. 132–152, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. Bin, L. Jibin, L. Yao, and R. Weiguo, “Bifurcations of travelling wave solutions for a variant of Camassa-Holm equation,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 222–232, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J. B. Li and Z. R. Liu, “Smooth and non-smooth traveling waves in a nonlinearly dispersive equation,” Applied Mathematical Modelling, vol. 25, pp. 41–56, 2000. View at Publisher · View at Google Scholar
  14. Q. Liu, Y. Zhou, and W. Zhang, “Bifurcation of travelling wave solutions for the modified dispersive water wave equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 1, pp. 151–166, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. Z. Liu and C. Yang, “The application of bifurcation method to a higher-order KdV equation,” Journal of Mathematical Analysis and Applications, vol. 275, no. 1, pp. 1–12, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. N. Chow and J. K. Hale, Methods of Bifurcation Theory, vol. 251, Springer, New York, NY, USA, 1982.
  17. Z. F. Zhang, T. R. Ding, W. Z. Huang, and Z. X. Dong, Qualitative Theory of Differential Equations, vol. 101 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1992.
  18. 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
  19. 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