×
Xin, Hua

The exponential function rational expansion method and exact solutions to nonlinear lattice equations system. (English) Zbl 1207.34097

Appl. Math. Comput. 217, No. 4, 1561-1565 (2010).
Summary: We propose an exponential function rational expansion method for solving exact traveling wave solutions to systems of nonlinear differential-difference equations. By this method, we obtain some exact traveling wave solutions to a system of relativistic Toda lattice equations and discuss the significance of these solutions. Finally, we give an open problem.

Cited in 3 Documents

MSC:

34K31 Lattice functional-differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations

Keywords:

differential-difference equation; exact solution; traveling wave solution; exponential function rational expansion method

Software:

DDESpecialSolutions
PDF BibTeX XML Cite
\textit{H. Xin}, Appl. Math. Comput. 217, No. 4, 1561--1565 (2010; Zbl 1207.34097)
Full Text: DOI

References:

[1] Toda, M., Theory of Nonlinear Lattices (1981), Springer: Springer Berlin · Zbl 0465.70014
[2] Tsuchida, T.; Ujino, H.; Wadati, M., Integrable semi-discretization of the coupled modified KdV equations, J. Math. Phys., 39, 4785-4813 (1998) · Zbl 0933.35176
[3] Tsuchida, T.; Ujino, H.; Wadati, M., Integrable semi-discretization of the coupled nonlinear Schrodinger equations, J. Phys. A: Math. Gen., 32, 2239-2261 (1999) · Zbl 0941.35112
[4] Baldwin, D.; Göktas, Ü.; Hereman, W., Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations, Comput. Phys. Commun., 163, 203-222 (2004) · Zbl 1196.68324
[5] Zhu, Jia-Min, Hyperbolic function method for solving nonlinear differential-different equations, Chin. Phys., 14, 1290-1295 (2005)
[6] Yang, Zhonghang; Hou, Y. C., A generalized coth-function method for exact solution of differential-difference equation, Chaos, Solitons and Fractals, 33, 1642-1651 (2007)
[7] Dai, Chao-Qin; Zhang, Jie-Fang, Traveling wave solutions to the coupled discrete nonlinear Schrodinger equations, Int. J. Mod. Phys. B, 19, 2129-2143 (2005) · Zbl 1101.81048
[8] Cheng-shi, Liu, Exponential function rational expansion method for nonlinear differential-difference equations, Chaos, Solitons and Fractals, 40, 708-716 (2009) · Zbl 1197.35243
[9] Cheng-shi, Liu, Representations and classification of traveling wave solutions to Sinh-Gordon equation, Commoun. Theor. Phys., 49, 153-158 (2008) · Zbl 1392.35063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.