Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 974050, 8 pages
http://dx.doi.org/10.1155/2014/974050
Research Article

Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

1School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
2School of Science, Beijing Information Science and Technology University, Beijing 100192, China
3China Petroleum Engineering and Construction Corp., Beijing 100028, China

Received 8 February 2014; Accepted 30 March 2014; Published 24 April 2014

Academic Editor: Christian Maes

Copyright © 2014 Jing Chen 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. C. Itzykson and J. B. Zuber, Quantum Field Theory, McGraw-Hill, New York, NY, USA, 1980. View at MathSciNet
  2. V. V. Tsegel’nik, “Self-similar solutions of a system of two nonlinear partial differential equations,” Differential Equations, vol. 36, no. 3, pp. 480–482, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. G. Thornhill and D. ter Haar, “Langmuir turbulence and modulational instability,” Physics Reports, vol. 43, no. 2, pp. 43–99, 1978. View at Google Scholar · View at Scopus
  4. R. O. Dendy, Plama Dynamics, Oxford University Press, Oxford, UK, 1990.
  5. Y.-P. Wang and D.-F. Xia, “Generalized solitary wave solutions for the Klein-Gordon-Schrödinger equations,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2300–2306, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. Shang, Y. Huang, and W. Yuan, “New exact traveling wave solutions for the Klein-Gordon-Zakharov equations,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1441–1450, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Liu, Z. Fu, S. Liu, and Z. Wang, “The periodic solutions for a class of coupled nonlinear Klein-Gordon equations,” Physics Letters: A, vol. 323, no. 5-6, pp. 415–420, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Wang, J. Chen, and L. Zhang, “Conservative difference methods for the Klein-Gordon-Zakharov equations,” Journal of Computational and Applied Mathematics, vol. 205, no. 1, pp. 430–452, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. D.-S. Wang, “A class of special exact solutions of some high dimensional non-linear wave equations,” International Journal of Modern Physics B: Condensed Matter Physics. Statistical Physics. Applied Physics, vol. 24, no. 23, pp. 4563–4579, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. D.-S. Wang, Z. Yan, and H. Li, “Some special types of solutions of a class of the (N+1)-dimensional nonlinear wave equations,” Computers & Mathematics with Applications, vol. 56, no. 6, pp. 1569–1579, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Z. Yan, “Separation transformation and envelope solutions of the higher-dimensional complex nonlinear Klein-Gordon equation,” Physica Scripta, vol. 75, no. 3, pp. 320–322, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Z. Yan, “Similarity transformations and exact solutions for a family of higher-dimensional generalized Boussinesq equations,” Physics Letters: A, vol. 361, no. 3, pp. 223–230, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Liu, J. Chen, W. Hu, and L.-L. Zhu, “Separation transformation and new exact solutions for the (1+N)-dimensional triple Sine-Gordon equation,” Zeitschrift fur Naturforschung A: Journal of Physical Sciences, vol. 66, no. 1-2, pp. 19–23, 2011. View at Google Scholar · View at Scopus
  14. Y. Tian, J. Chen, and Z.-F. Zhang, “Separation transformation and new exact solutions of the (N+1)-dimensional dispersive double sine-Gordon equation,” Communications in Theoretical Physics, vol. 58, no. 3, pp. 398–404, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. D. Wang and H.-Q. Zhang, “Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation,” Chaos, Solitons and Fractals, vol. 25, no. 3, pp. 601–610, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  16. D. Wang and H.-Q. Zhang, “Symbolic computation and non-travelling wave solutions of the (2+1)-dimensional korteweg de vries equation,” Zeitschrift fur Naturforschung A: Journal of Physical Sciences, vol. 60, no. 4, pp. 221–228, 2005. View at Google Scholar · View at Scopus
  17. M. Wang and X. Li, “Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1257–1268, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. Abramowitz and I. A. Stegun, Hand Book of Mathematical Functions, Dover, New York, NY, USA, 1965.
  19. D.-S. Wang, X.-H. Hu, J. Hu, and W. M. Liu, “Quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 81, no. 2, Article ID 025604, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. D.-S. Wang, S.-W. Song, B. Xiong, and W. M. Liu, “Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 84, no. 5, Article ID 053607, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. D. S. Wang, X. Zeng, and Y. Q. Ma, “Exact vortex solitons in a quasi-two-dimensional Bose- Einstein condensate with spatially inhomogeneous cubic-quintic nonlinearity,” Physics Letters A, vol. 376, no. 45, pp. 3067–3070, 2012. View at Google Scholar
  22. D. S. Wang and X. G. Li, “Localized nonlinear matter waves in a Bose C Einstein condensate with spatially inhomogeneous two- and three-body interactions,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 45, no. 10, Article ID 105301, 2012. View at Google Scholar
  23. D. S. Wang, Y. R. Shi, K. W. Chow, Z. X. Yu, and X. G. Li, “Matter-wave solitons in a spin-1 Bose-Einstein condensate with time-modulated external potential and scattering lengths,” European Physical Journal D, vol. 67, article 242, 2013. View at Google Scholar