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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 842394, 11 pages
http://dx.doi.org/10.1155/2012/842394
Research Article

Abundant Interaction Solutions of Sine-Gordon Equation

1School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
2Department of Basic Science, Gengdan Institute of Beijing University of Technology, Beijing 101301, China

Received 15 July 2012; Accepted 2 October 2012

Academic Editor: Junjie Wei

Copyright © 2012 DaZhao Lü 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. A. Seeger, H. Donth, and A. Kochendörfer, “Theorie der Versetzungen in eindimensionalen Atomreihen. III. Versetzungen, Eigenbewegungen und ihre Wechselwirkung,” Zeitschrift für Physik. C, vol. 134, pp. 173–193, 1953. View at Zentralblatt MATH
  2. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer Series in Nonlinear Dynamics, Springer, Berlin, Germany, 1991.
  3. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “Method for solving the sine-Gordon equation,” Physical Review Letters, vol. 30, pp. 1262–1264, 1973. View at Publisher · View at Google Scholar
  4. R. Hirota and J. Satsuma, “A simple structure of superposition formula of the backlund transformation,” Journal of the Physical Society of Japan, vol. 45, no. 5, pp. 1741–1750, 1978. View at Scopus
  5. S. Y. Lou, H. C. Hu, and X. Y. Tang, “Interactions among periodic waves and solitary waves of the (N+l)-dimensional sine-Gordon field,” Physical Review E, vol. 71, no. 3, Article ID 036604, 8 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. J. J. C. Nimmo and N. C. Freeman, “The use of Bäcklund transformations in obtaining N-soliton solutions in Wronskian form,” Journal of Physics A, vol. 17, no. 7, pp. 1415–1424, 1984. View at Publisher · View at Google Scholar
  7. A. V. Bäcklund, “Über flachen Transformationen,” Mathematische Annalen, vol. 9, pp. 297–320, 1876.
  8. A. V. Bäcklund, “Zur theorie der Flachentransformationen,” Mathematische Annalen, vol. 19, pp. 387–422, 1882.
  9. J. K. Perring and T. H. R. Skyrme, “A model unified field equation,” Nuclear Physics. B, vol. 31, pp. 550–555, 1962. View at Publisher · View at Google Scholar
  10. A. Barone, F. Esposito, C. J. Magee, and A. C. Scott, “Theory and applications of the Sine-Gordon equation,” La Rivista del Nuovo Cimento, vol. 1, no. 2, pp. 227–267, 1971. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Frenkel and T. Kontorova, “On the theory of plastic deformation and twinning,” Journal of Physics-USSR, vol. 1, pp. 137–149, 1939. View at Zentralblatt MATH
  12. G. L. Lamb, Jr., “Analytical descriptions of ultrashort optical pulse propagation in a resonant medium,” Reviews of Modern Physics, vol. 43, pp. 99–124, 1971. View at Publisher · View at Google Scholar
  13. B. D. Josephson, “Possible new effects in superconductive tunnelling,” Physics Letters, vol. 1, no. 7, pp. 251–253, 1962. View at Scopus
  14. J. L. Fergason and G. H. Brown, “Liquid crystals and living systems,” Journal of the American Oil Chemists Society, vol. 45, no. 3, pp. 120–127, 1968. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Wang, Elimination Methods, Texts and Monographs in Symbolic Computation, Springer, New York, NY, USA, 2001. View at Publisher · View at Google Scholar
  16. S. K. Liu, Z. Fu, S. 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
  17. Z. Yan, “The new extended Jacobian elliptic function expansion algorithm and its applications in nonlinear mathematical physics equations,” Computer Physics Communications, vol. 153, no. 2, pp. 145–154, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. W. Malfliet, “Solitary wave solutions of nonlinear wave equations,” American Journal of Physics, vol. 60, no. 7, pp. 650–654, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. C. Yan, “A simple transformation for nonlinear waves,” Physics Letters A, vol. 224, no. 1-2, pp. 77–84, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. E. Fan, “Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics,” Chaos, Solitons and Fractals, vol. 16, no. 5, pp. 819–839, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. Y.-Z. Peng, “Exact solutions for some nonlinear partial differential equations,” Physics Letters A, vol. 314, no. 5-6, pp. 401–408, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. Y. Chen and Q. Wang, “Multiple Riccati equations rational expansion method and complexiton solutions of the Whitham-Broer-Kaup equation,” Physics Letters A, vol. 347, no. 4-6, pp. 215–227, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. E. Yomba, “Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schrödinger equations,” Physics Letters A, vol. 372, no. 10, pp. 1612–1618, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. E. M. E. Zayed, “New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G'/G)-expansion method,” Journal of Physics A, vol. 42, no. 19, Article ID 195202, 13 pages, 2009. View at Publisher · View at Google Scholar
  26. W.-X. Ma, H. Wu, and J. He, “Partial differential equations possessing Frobenius integrable decompositions,” Physics Letters A, vol. 364, no. 1, pp. 29–32, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. W.-X. Ma and J.-H. Lee, “A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation,” Chaos, Solitons & Fractals, vol. 42, no. 3, pp. 1356–1363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH