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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 158142, 8 pages
http://dx.doi.org/10.1155/2009/158142
Research Article

Application of Symbolic Computation in Nonlinear Differential-Difference Equations

1Department of Computer Science, Liaoning Normal University, Liaoning, Dalian 116081, China
2Key Laboratory of Mathematics and Mechanization (KLMM), Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, China
3School of Physics and Electronic Technology, Liaoning Normal University, Liaoning, Dalian 116029, China

Received 18 March 2009; Accepted 12 September 2009

Academic Editor: Yong Zhou

Copyright © 2009 Fuding Xie 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. M. Wadati, “Transformation theories for nonlinear discrete systems,” Progress of Theoretical Physics Supplement, vol. 59, pp. 36–63, 1976. View at Publisher · View at Google Scholar
  2. M. Wadati, “Wave propagation in nonlinear lattice—I,” Journal of the Physical Society of Japan, vol. 38, pp. 673–680, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  3. D. Baldwin, Ü Göktas, and W. Hereman, “Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations,” Computer Physics Communications, vol. 162, no. 3, pp. 203–217, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. Ü Göktas and W. Hereman, “Computation of conservation laws for nonlinear lattices,” Physica D, vol. 123, no. 1–4, pp. 425–436, 1998. View at Google Scholar · View at Scopus
  5. V. E. Adler, S. I. Svinolupov, and R. I. Yamilov, “Multi-component Volterra and Toda type integrable equations,” Physics Letters A, vol. 254, no. 1-2, pp. 24–36, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. J. Ablowitz and J. F. Ladik, “Nonlinear differential-difference equations,” Journal of Mathematical Physics, vol. 16, no. 3, pp. 598–603, 1975. View at Google Scholar · View at Scopus
  7. M. Toda, Theory of Nonlinear Lattices, Springer, Berlin, Germany, 1988.
  8. X.-B. Hu and W.-X. Ma, “Application of Hirota's bilinear formalism to the Toeplitz lattice—some special soliton-like solutions,” Physics Letters A, vol. 293, no. 3-4, pp. 161–165, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H.-W. Tam and X.-B. Hu, “Soliton solutions and Bäcklund transformation for the Kupershmidt five-field lattice: a bilinear approach,” Applied Mathematics Letters, vol. 15, no. 8, pp. 987–993, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Y. Lou, “Generalized symmetries and W algebras in three-dimensional Toda field theory,” Physical Review Letters, vol. 71, no. 25, pp. 4099–4102, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. E. Elmer and E. S. Van Vleck, “A variant of Newton's method for the computation of traveling waves of bistable differential-difference equations,” Journal of Dynamics and Differential Equations, vol. 14, no. 3, pp. 493–517, 2002. View at Google Scholar · View at Scopus
  12. W. T. Wu, Polynomial Equation-Solving and Its Application, Algorithms and Computation, Springer, Berlin, Germany, 1994.