Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
International Journal of Differential Equations
Volume 2012 (2012), Article ID 596762, 11 pages
doi:10.1155/2012/596762
Research Article
The Improved Riccati Equation Method and Exact Solutions to mZK Equation
College of Physics and Material Science, Anhui University, Hefei, Anhui 230039, China
Received 26 May 2012; Accepted 24 July 2012
Academic Editor: Giovany M. Figueiredo
Copyright © 2012 Xiaofeng Li. 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
- B. Tian and Y. T. Gao, “Spherical nebulons and Backlund transformation for a space or laboratory un-magnetized dusty plasma with symbolic computation,” The European Physical Journal D, vol. 33, pp. 59–65, 2005.
- L. Tian and J. Yin, “Stability of multi-compacton solutions and Bäcklund transformation in ,” Chaos, Solitons and Fractals, vol. 23, no. 1, pp. 159–169, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J.-H. He and L.-N. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method,” Physics Letters A, vol. 372, no. 7, pp. 1044–1047, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- L. WangM, Y. B. Zhou, and Z. B. Li, “Application of homogeneous balance method to exact solutions of nonlinear equations in mathematical physics,” Physics Letters A, vol. 216, pp. 67–75, 1996.
- M. H. M. Moussa and R. M. El Shikh, “Two applications of the homogeneous balance method for solving the generalized Hirota-Satsuma coupled KdV system with variable coefficients,” International Journal of Nonlinear Science, vol. 7, no. 1, pp. 29–38, 2009. View at Zentralblatt MATH
- A. A. Soliman, “The modified extended tanh-function method for solving Burgers-type equations,” Physica A, vol. 361, no. 2, pp. 394–404, 2006. View at Publisher · View at Google Scholar
- M. A. Abdou and A. A. Soliman, “Modified extended tanh-function method and its application on nonlinear physical equations,” Physics Letters A, vol. 353, pp. 487–492, 2006.
- S. K. Liu, Z. T. Fu, S. D. 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
- Z. T. Fu, S. K. Liu, S. D. 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
- M. Wang, X. Li, and J. Zhang, “The -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
- A. Bekir, “Application of the -expansion method for nonlinear evolution equations,” Physics Letters A, vol. 372, no. 19, pp. 3400–3406, 2008. View at Publisher · View at Google Scholar
- S. Munro and E. J. Parkes, “The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions,” Journal of Plasma Physics, vol. 62, no. 3, pp. 305–317, 1999.
- S. Munro and E. J. Parkes, “Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation,” Journal of Plasma Physics, vol. 64, no. 4, pp. 411–426, 2000.
- A. de Bouard, “Stability and instability of some nonlinear dispersive solitary waves in higher dimension,” Proceedings of the Royal Society of Edinburgh Section A, vol. 126, no. 1, pp. 89–112, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- F. Linares and A. Pastor, “Local and global well-posedness for the 2D generalized Zakharov-Kuznetsov equation,” Journal of Functional Analysis, vol. 260, no. 4, pp. 1060–1085, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- F. Ribaud and S. Vento, “A note on the Cauchy problem for the 2D generalized Zakharov-Kuznetsov equations,” Comptes Rendus Mathématique, vol. 350, no. 9-10, pp. 499–503, 2012. View at Publisher · View at Google Scholar
- F. Linares and A. Pastor, “Well-posedness for the two-dimensional modified Zakharov-Kuznetsov equation,” SIAM Journal on Mathematical Analysis, vol. 41, no. 4, pp. 1323–1339, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH