- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 863583, 10 pages
The GDTM-Padé Technique for the Nonlinear Lattice Equations
Hangzhou Institute of Commerce, Zhejiang Gongshang University, Hangzhou 310018, China
Received 22 December 2011; Accepted 28 January 2012
Academic Editor: Shaher Momani
Copyright © 2012 Junfeng Lu. 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.
- 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.
- D. Baldwin, Ü. Göktaş, 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.
- L. Bonora and C. S. Xiong, “An alternative approach to KP hierarchy in matrix models,” Physics Letters B, vol. 285, no. 3, pp. 191–198, 1992.
- E. Fermi, J. Pasta, and S. Ulam, The Collected Papers of Enrico Fermi, The University of Chicago Press, Chicago, Ill, USA, 1965.
- R. Hirota and M. Iwao, “Time-discretization of soliton equations,” in SIDE III-Symmetries and Integrability of Difference Equations, vol. 25 of CRM Proceedings & Lecture Notes, pp. 217–229, American Mathematical Society, Providence, RI, USA, 2000.
- D. Levi and O. Ragnisco, “Extension of the spectral-transform method for solving nonlinear differential difference equations,” Lettere al Nuovo Cimento, vol. 22, no. 17, pp. 691–696, 1978.
- D. Levi and R. Yamilov, “Conditions for the existence of higher symmetries of evolutionary equations on the lattice,” Journal of Mathematical Physics, vol. 38, no. 12, pp. 6648–6674, 1997.
- Y. B. Suris, “New integrable systems related to the relativistic Toda lattice,” Journal of Physics A, vol. 30, no. 5, pp. 1745–1761, 1997.
- Y. B. Suris, “On some integrable systems related to the Toda lattice,” Journal of Physics A, vol. 30, no. 6, pp. 2235–2249, 1997.
- Y. B. Suris, “Integrable discretizations for lattice system: local equations of motion and their Hamiltonian properties,” Reviews in Mathematical Physics, vol. 11, no. 6, pp. 727–822, 1999.
- R. I. Yamilov, “Construction scheme for discrete Miura transformations,” Journal of Physics A, vol. 27, no. 20, pp. 6839–6851, 1994.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, vol. 60 of Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994.
- G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988.
- C. Dai and J. Zhang, “Jacobian elliptic function method for nonlinear differential-difference equations,” Chaos, Solitons & Fractals, vol. 27, no. 4, pp. 1042–1047, 2006.
- J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 30, no. 3, pp. 700–708, 2006.
- M. Wang, X. Li, and J. Zhang, “The -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008.
- S. Zhang and H.-Q. Zhang, “Variable-coefficient discrete tanh method and its application to -dimensional Toda equation,” Physics Letters A, vol. 373, no. 33, pp. 2905–2910, 2009.
- V. S. Erturk, S. Momani, and Z. Odibat, “Application of generalized differential transform method to multi-order fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1642–1654, 2008.
- S. Momani, Z. Odibat, and V. S. Erturk, “Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation,” Physics Letters A, vol. 370, no. 5-6, pp. 379–387, 2007.
- Z. Odibat, S. Momani, and V. S. Erturk, “Generalized differential transform method: application to differential equations of fractional order,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 467–477, 2008.
- Z. Li, W. Zhen, and Z. Zhi, “Generalized differential transform method to differential-difference equation,” Physics Letters A, vol. 373, no. 45, pp. 4142–4151, 2009.
- H. Aratyn, L. A. Ferreira, J. F. Gomes, and A. H. Zimerman, “On two-current realization of KP hierarchy,” Nuclear Physics B, vol. 402, no. 1-2, pp. 85–117, 1993.
- G. A. Baker, Essential of Padé Approximants, Academic Press, London, UK, 1975.
- G. A. Baker and P. Graves-Morris, Encyclopedia of Mathematics and its Application 13, Parts I and II: Padé Approximants, Addison-Wesley Publishing Company, New York, NY, USA, 1981.