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Advances in Mathematical Physics

Volume 2014 (2014), Article ID 217393, 11 pages

http://dx.doi.org/10.1155/2014/217393

Research Article

## Two Conservative Difference Schemes for Rosenau-Kawahara Equation

^{1}School of Mathematics, Sichuan University, Chengdu 610064, China^{2}School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China

Received 14 September 2013; Revised 22 December 2013; Accepted 7 January 2014; Published 18 March 2014

Academic Editor: Ricardo Weder

Copyright © 2014 Jinsong Hu 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

- P. Rosenau, “A quasi-continuous description of a nonlinear transmission line,”
*Physica Scripta*, vol. 34, pp. 827–829, 1986. View at Google Scholar - P. Rosenau, “Dynamics of dense discrete systems,”
*Progress of Theoretical Physics*, vol. 79, pp. 1028–1042, 1988. View at Google Scholar - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - M. Labidi and A. Biswas, “Application of He’s principles to Rosenau-Kawahara equation,”
*Mathematics in Engineering, Science and Aerospace MESA*, vol. 2, no. 2, pp. 183–197, 2011. View at Google Scholar - A. Biswas, H. Triki, and M. Labidi, “Bright and dark solitons of the Rosenau-Kawahara equation with power law nonlinearity,”
*Physics of Wave Phenomena*, vol. 19, no. 1, pp. 24–29, 2011. View at Publisher · View at Google Scholar · View at Scopus - T. Wang, L. Zhang, and F. Chen, “Conservative schemes for the symmetric regularized long wave equations,”
*Applied Mathematics and Computation*, vol. 190, no. 2, pp. 1063–1080, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Li and L. Vu-Quoc, “Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation,”
*SIAM Journal on Numerical Analysis*, vol. 32, no. 6, pp. 1839–1875, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Q. Chang, E. Jia, and W. Sun, “Difference schemes for solving the generalized nonlinear Schrödinger equation,”
*Journal of Computational Physics*, vol. 148, no. 2, pp. 397–415, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T.-C. Wang and L.-M. Zhang, “Analysis of some new conservative schemes for nonlinear Schrödinger equation with wave operator,”
*Applied Mathematics and Computation*, vol. 182, no. 2, pp. 1780–1794, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. Wang, B. Guo, and L. Zhang, “New conservative difference schemes for a coupled nonlinear Schrödinger system,”
*Applied Mathematics and Computation*, vol. 217, no. 4, pp. 1604–1619, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - L. Zhang, “A finite difference scheme for generalized regularized long-wave equation,”
*Applied Mathematics and Computation*, vol. 168, no. 2, pp. 962–972, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Z. Fei and L. Vázquez, “Two energy conserving numerical schemes for the sine-Gordon equation,”
*Applied Mathematics and Computation*, vol. 45, no. 1, pp. 17–30, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Y. S. Wong, Q. Chang, and L. Gong, “An initial-boundary value problem of a nonlinear Klein-Gordon equation,”
*Applied Mathematics and Computation*, vol. 84, no. 1, pp. 77–93, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - Q. S. Chang, B. L. Guo, and H. Jiang, “Finite difference method for generalized Zakharov equations,”
*Mathematics of Computation*, vol. 64, no. 210, pp. 537–553, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Hu and K. Zheng, “Two conservative difference schemes for the generalized Rosenau equation,”
*Boundary Value Problems*, vol. 2010, Article ID 543503, 18 pages, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - X. Pan and L. Zhang, “On the convergence of a conservative numerical scheme for the usual Rosenau-RLW equation,”
*Applied Mathematical Modelling*, vol. 36, no. 8, pp. 3371–3378, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - X. Pan and L. Zhang, “Numerical simulation for general Rosenau-RLW equation: an average linearized conservative scheme,”
*Mathematical Problems in Engineering*, vol. 2012, Article ID 517818, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - F. E. Browder, “Existence and uniqueness theorems for solutions of nonlinear boundary value problems,” in
*Proceedings of Symposia in Applied Mathematics*, vol. 17, pp. 24–49, 1965. - T. Wang and B. Guo, “A robust semi-explicit difference scheme for the Kuramoto-Tsuzuki equation,”
*Journal of Computational and Applied Mathematics*, vol. 233, no. 4, pp. 878–888, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Hu, B. Hu, and Y. Xu, “C-N difference schemes for dissipative symmetric regularized long wave equations with damping term,”
*Mathematical Problems in Engineering*, vol. 2011, Article ID 651642, 16 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet