Printer Friendly

Extended Riccati sub-ODE method for solving nonlinear differential-difference equations.

Received: August 13, 2012. Revised: October 29, 2012.

2010 Mathematics Subject Classification: 35Q92, 39A12.


[1] E. Fermi, J. Pasta, and S. Ulam: Collected Papers of Enrico Fermi II, Univer of Chicago Press, Chicago, 1965.

[2] M. Wadati: Transformation theories for nonlinear discrete systems, Prog. Suppl. Theor. Phys., 59(1976), 36-63.

[3] M. K. Kadalbajoo, and K. K. Sharma: Numerical treatment for singularly perturbed nonlinear differential difference equations with negative shift, Nonlinear Anal., 63(2005), e1909-e1924.

[4] M. Toda: Theory of Nonlinear Lattices, Springer, Berlin, 1981.

[5] D. Baldwin, U. Goktas, and W. Hereman: Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations, Comput. Phys. Commun., 162(2004), 203-217.

[6] M. J. Ablowitz, and J. Ladik: Nonlinear differential-difference equations, J. Math. Phys., 16(1975), 598-603.

[7] S. K. Liu, Z. T. Fu, Z. G. Wang, and S. D. Liu: Periodic solutions for a class of nonlinear differential-difference equations, Commun. Theor. Phys., 49(2008), 1155-1158.

[8] L. Wu, L. D. Xie, and J. F. Zhang: Adomian decomposition method for nonlinear differential-difference equations, Commun. Nonlinear Sci. Numer. Simul., 14(2009), 12-18.

[9] P. Marquii, J. M. Bilbault, and M. Rernoissnet: Observation of nonlinear localized modes in an electrical lattice, Phys. Rev. E, 51(1995), 6127-6133.

[10] H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison: Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett., 81(1998), 3383-3386.

[11] I. Aslan: Discrete exact solutions to some nonlinear differential-difference equations via the (G'/G)-expansion method, Appl. Math. Comput., 215(2009), 3140-3147.

[12] B. Ayhan, and A. Bekir: The (G'/G)-expansion method for the nonlinear lattice equations, Commun. Nonlinear Sci. Numer. Simulat., 17(2012), 3490-3498.

[13] S. Zhang, L. Dong, J.M. Ba, and Y.N. Sun: The (G'/G)-expansion method for nonlinear differential-difference equations, Phys. Lett. A, 373(2009), 905-910.

[14] B. Tang, Y. N. He, L. L. Wei, and S. L. Wang: Variable-coefficient discrete (G'/G)-expansion method for nonlinear differential-difference equations, Phys. Lett. A, 375(2011), 3355-3361.

[15] C. Q. Dai, X. Cen, and S.S. Wu: Exact travelling wave solutions of the discrete sine-Gordon equation obtained via the exp-function method, Nonlinear Anal., 70(2009), 58-63.

[16] C. S. Liu: Exponential function rational expansion method for nonlinear differential-difference equations, Chaos, Solitons and Fractals, 40(2009), 708-716.

[17] H. Xin: The exponential function rational expansion method and exact solutions to nonlinear lattice equations system, Appl. Math. Comput., 217(2010), 1561-1565.

[18] K. A. Gepreel, and A. R. Shehata: Rational Jacobi elliptic solutions for nonlinear differential-difference lattice equations, Appl. Math. Lett., 25(2012), 1173-1178.

[19] W. H. Huang, and Y. L. Liu: Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrodinger system, Chaos, Solitons and Fractals, 40(2009), 786-792.

[20] X. B. Hu, and W. X. Ma: Application of Hirota's bilinear formalism to the Toeplitz lattice some special soliton-like solutions, Phys. Lett. A, 293(2002), 161C165.

[21] I. Aslan: A discrete generalization of the extended simplest equation method, Commun. Nonlinear Sci. Numer. Simul., 15(2010), 1967-1973.

[22] W. Zhen: Discrete tanh method for nonlinear difference-differential equations, Comput. Phys. Com mun., 180(2009), 1104-1108.

[23] N. A. Kudryashov: A note on the (G'/G)-expansion method, Appl. Math. Comput., 217(2010), 1755-1758.

Shandong University of Technology

School of Science

Zhangzhou Road 12, 255049, Zibo, China

E-mail address:
COPYRIGHT 2013 Fair Partners Team for the Promotion of Science
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2013 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Feng, Qinghua
Publication:Journal of Advanced Mathematical Studies
Article Type:Author abstract
Geographic Code:9CHIN
Date:Jan 1, 2013
Previous Article:Study on certain subclasses of analytic functions.
Next Article:Iterative approximation for common solution of a finite family of m-accretive operators.

Terms of use | Privacy policy | Copyright © 2019 Farlex, Inc. | Feedback | For webmasters