Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2013, Article ID 578094, 4 pages
http://dx.doi.org/10.1155/2013/578094
Research Article

On the Support of Solutions to a Two-Dimensional Nonlinear Wave Equation

1Taizhou Institute of Science and Technology, NUST, Taizhou, Jiangsu 225300, China
2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
3Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand 831014, India

Received 10 January 2013; Accepted 21 January 2013

Academic Editor: Ji Gao

Copyright © 2013 Wenbin Zhang 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. G. A. Gottwald, “The Zakharov-Kuznetsov equation as a twodimensional model for nonlinear Rossby wave,” http://arxiv.org/abs/nlin/0312009.
  2. J. H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. Fu, S. Liu, and S. Liu, “Multiple structures of two-dimensional nonlinear Rossby wave,” Chaos, Solitons and Fractals, vol. 24, no. 1, pp. 383–390, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. A. Aslan, “Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov-Kuznetsov equation,” Applied Mathematics and Computation, vol. 217, no. 4, pp. 1421–1429, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  5. V. E. Zakharov and E. A. Kuznetsov, “On three-dimensional solitons,” Journal of Experimental and Theoretical Physics, vol. 39, pp. 285–286, 1974. View at Google Scholar
  6. B. K. Shivamoggi, “The Painlevé analysis of the Zakharov-Kuznetsov equation,” Physica Scripta, vol. 42, no. 6, pp. 641–642, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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 · View at MathSciNet
  8. A. V. Faminskiĭ, “The Cauchy problem for the Zakharov-Kuznetsov equation,” Differential Equations, vol. 31, no. 6, pp. 1002–1012, 1995. View at Google Scholar · View at MathSciNet
  9. H. A. Biagioni and F. Linares, “Well-posedness results for the modified Zakharov-Kuznetsov equation,” in Nonlinear Equations: Methods, Models and Applications, vol. 54 of Progress in Nonlinear Differential Equations and Their Applications, pp. 181–189, Birkhäuser, Basel, Switzerland, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 · View at MathSciNet
  11. F. Linares, A. Pastor, and J.-C. Saut, “Well-posedness for the ZK equation in a cylinder and on the background of a KdV soliton,” Communications in Partial Differential Equations, vol. 35, no. 9, pp. 1674–1689, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Panthee, “A note on the unique continuation property for Zakharov-Kuznetsov equation,” Nonlinear Analysis. Theory, Methods & Applications, vol. 59, no. 3, pp. 425–438, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Bustamante, P. Isaza, and J. Mejía, “On the support of solutions to the Zakharov-Kuznetsov equation,” Journal of Differential Equations, vol. 251, no. 10, pp. 2728–2736, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. Bourgain, “On the compactness of the support of solutions of dispersive equations,” International Mathematics Research Notices, no. 9, pp. 437–447, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. E. Kenig, G. Ponce, and L. Vega, “On the support of solutions to the generalized KdV equation,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 19, no. 2, pp. 191–208, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet