Abstract
In this paper, we generalize the extended tanh-function approach, which used to find new exact travelling wave solutions of nonlinear partial differential equations (NPDES) or coupled nonlinear partial differential equations, to nonlinear differential-difference equations (NDDES). As illustration, we discuss some Toda lattice equations, and solitary wave and periodic wave solutions of these Toda lattice equations are obtained by means of the extended tanh-function approach.
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References
Ablowitz, M. J. (1978). Studies in Applied Mathematics 58, 17.
Baldwin, D., Göktas, ü., and Hereman, W. (2004). Computer Physics Communications 162, 203.
Dai, C. Q. and Zhang, J. F. (2006). Chaos, Solitons and Fractals 27, 1042.
Dai, C. Q., Yang, Q., and Zhang, J. F. (2004). Znaturforsch A 59, 635.
Fan, E. G. (2000). Physics Letters A 277, 212.
Fermi, E., Pasta, J., and Ulam, S. (1965). Collected Papers of Enrico Fermi II, University of Chicago Press, Chicago.
Hickman, M. and Hereman, W. (2003). Proceedings of the Royal Society of London A 459, 2705.
Kajiwara, K. and Satsuma, J. (1991). Journal of Mathematical Physics 32, 506–514.
Qian, X. M., Lou, S. Y., and Hu, X. B. (2003). Journal of Physics A: Mathematical and General 37, 2401.
Qian, X. M., Lou, S. Y., and Hu, X. B. (2004). Znaturforsch A 59, 645.
Suris, Y. B. (1997). Journal of Physics A: Mathematical and General 30, 1745.
Suris, Y. B. (1998). Miura transformations for Toda-type integrable systems, with applications to the problem of integrable discretizations, Preprint 367, Sfb 288, Fachbereich Mathematik, Technische Universität, Berlin.
Teschl, G. (2000). Jacobi Operators and Completely Integrable Nonlinear Lattices (Rhode Island: AMS Mathematical Surveys and Monographs 72, AMS, Providence).
Toda, M. (1981). Theory of Nonlinear Lattices, Springer-Verlag, Berlin.
Zheng, C. L., Fang, J. P., and Chen, L. Q. (2005). Chaos, Solitons and Fractals 23, 1741.
Zhu, J. M. (2005). Chinese Physics 14, 1290.
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PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik.
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Dai, C., Ni, Y. The Application of Extended Tanh-Function Approach in Toda Lattice Equations. Int J Theor Phys 46, 1455–1465 (2007). https://doi.org/10.1007/s10773-006-9285-y
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DOI: https://doi.org/10.1007/s10773-006-9285-y