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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 202793, 9 pages
http://dx.doi.org/10.1155/2014/202793
Research Article

An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation

1Chengdu Technological University, Chengdu 610031, China
2School of Mathematics and Computer Science, Yangtze Normal University, Chongqing 408100, China

Received 14 June 2013; Accepted 7 January 2014; Published 25 February 2014

Academic Editor: Anjan Biswas

Copyright © 2014 Maobo Zheng and Jun Zhou. 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. Y. Cui and D. K. Mao, “Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation,” Journal of Computational Physics, vol. 227, no. 1, pp. 376–399, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Zhu and J. Zhao, “The alternating segment explicit-implicit scheme for the dispersive equation,” Applied Mathematics Letters, vol. 14, no. 6, pp. 657–662, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. R. Bahadır, “Exponential finite-difference method applied to Korteweg-de Vries equation for small times,” Applied Mathematics and Computation, vol. 160, no. 3, pp. 675–682, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Özer and S. Kutluay, “An analytical-numerical method for solving the Korteweg-de Vries equation,” Applied Mathematics and Computation, vol. 164, no. 3, pp. 789–797, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. Rosenau, “A quasi-continuous description of a nonlinear transmission line,” Physica Scripta, vol. 34, pp. 827–829, 1986. View at Publisher · View at Google Scholar
  6. P. Rosenau, “Dynamics of dense discrete systems,” Progress of Theoretical Physics, vol. 79, pp. 1028–1042, 1988. View at Google Scholar
  7. M. A. Park, “On the Rosenau equation,” Matemática Aplicada e Computacional, vol. 9, no. 2, pp. 145–152, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. K. Chung and S. N. Ha, “Finite element Galerkin solutions for the Rosenau equation,” Applicable Analysis, vol. 54, no. 1-2, pp. 39–56, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. K. Omrani, F. Abidi, T. Achouri, and N. Khiari, “A new conservative finite difference scheme for the Rosenau equation,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 35–43, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. K. Chung, “Finite difference approximate solutions for the Rosenau equation,” Applicable Analysis, vol. 69, no. 1-2, pp. 149–156, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. K. Chung and A. K. Pani, “Numerical methods for the Rosenau equation,” Applicable Analysis, vol. 77, no. 3-4, pp. 351–369, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. A. V. Manickam, A. K. Pani, and S. K. Chung, “A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation,” Numerical Methods for Partial Differential Equations, vol. 14, no. 6, pp. 695–716, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. D. Kim and H. Y. Lee, “The convergence of finite element Galerkin solution for the Roseneau equation,” The Korean Journal of Computational & Applied Mathematics, vol. 5, no. 1, pp. 171–180, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. M. Zuo, “Solitons and periodic solutions for the Rosenau-KdV and Rosenau-Kawahara equations,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 835–840, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. Hu, Y. Xu, and B. Hu, “Conservative linear difference scheme for Rosenau-KdV equation,” Advances in Mathematical Physics, vol. 2013, Article ID 423718, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Esfahani, “Solitary wave solutions for generalized Rosenau-KdV equation,” Communications in Theoretical Physics, vol. 55, no. 3, pp. 396–398, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. Razborova, H. Triki, and A. Biswas, “Perturbation of dispersive shallow water waves,” Ocean Engineering, vol. 63, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  18. G. Ebadi, A. Mojaver, H. Triki, A. Yildirim, and A. Biswas, “Topological solitons and other solutions of the Rosenau-KdV equation with power law nonlinearity,” Romanian Journal of Physics, vol. 58, no. 1-2, pp. 3–14, 2013. View at Google Scholar · View at MathSciNet
  19. A. Saha, “Topological 1-soliton solutions for the generalized Rosenau-KdV equation,” Fundamental Journal of Mathematical Physics, vol. 2, no. 1, pp. 19–23, 2012. View at Google Scholar
  20. A. Chowdhury and A. Biswas, “Singular solitons and numerical analysis of Φ-four equation,” Mathematical Sciences, vol. 6, article 42, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. P. Suarez, S. Johnson, and A. Biswas, “Chebyshev split-step scheme for the sine-Gordon equation in 2+1 dimensions,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 14, no. 1, pp. 69–75, 2013. View at Google Scholar · View at MathSciNet
  22. M. A. Christou, “Christov-galerkin expansion for localized solutions in model equations with higher order dispersion,” in Proceedings of the 33rd International Conference on Applications of Mathematics in Engineering and Economics, M. D. Todorov, Ed., CP946, pp. 91–98, June 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. L. Zhou, Applications of Discrete Functional Analysis to the Finite Difference Method, International Academic Publishers, Beijing, China, 1991. View at MathSciNet