Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations. A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Through discussion and example, parallels are drawn to the tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation issues, scope, and limitations of the software are addressed.

References in zbMATH (referenced in 35 articles , 1 standard article )

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  1. Sirisubtawee, Sekson; Koonprasert, Sanoe: Exact traveling wave solutions of certain nonlinear partial differential equations using the (\left(G^\prime/ G^2\right))-expansion method (2018)
  2. Sirisubtawee, Sekson; Koonprasert, Sanoe; Khaopant, Chaowanee; Porka, Wanassanun: Two reliable methods for solving the (3 + 1)-dimensional space-time fractional Jimbo-Miwa equation (2017)
  3. Aslan, İsmail: Traveling waves of DDEs with rational nonlinearity (2016)
  4. Bekir, Ahmet; Güner, Özkan; Ayhan, Burcu: Exact solutions of some systems of fractional differential-difference equations (2015)
  5. Aslan, İsmail: Construction of exact solutions for fractional-type difference-differential equations via symbolic computation (2013)
  6. Gepreel, Khaled A.; Nofal, Taher A.; Alotaibi, Fawziah M.: Exact solutions for nonlinear differential difference equations in mathematical physics (2013)
  7. Meng, Fanwei: A new variable-coefficient Riccati subequation method for solving nonlinear lattice equations (2013)
  8. Wang, Qi: Extended rational expansion method for differential-difference equation (2013)
  9. Aslan, Ịsmail: The discrete ((G^\prime/G))-expansion method applied to the differential-difference Burgers equation and the relativistic Toda lattice system (2012)
  10. Aslan, İsmail: Some exact solutions for Toda type lattice differential equations using the improved (G(^\prime)/G)-expansion method (2012)
  11. Dimitrova, Zlatinka: On traveling waves in lattices: the case of Riccati lattices (2012)
  12. Feng, Yang; Dong, Yan-cheng: Symmetrical Lucas functions for the solutions of the lattice equation (2012)
  13. Gepreel, Khaled A.; Nofal, Taher A.; Al-Thobaiti, Ali A.: The modified rational Jacobi elliptic functions method for nonlinear differential difference equations (2012)
  14. Gepreel, Khaled A.; Shehata, A. R.: Jacobi elliptic solutions for nonlinear differential difference equations in mathematical physics (2012)
  15. He, Ji-Huan; Elagan, S. K.; Wu, Guo-Cheng: Solitary-solution formulation for differential-difference equations using an ancient Chinese algorithm (2012)
  16. Lu, Junfeng: The GDTM-Padé technique for the nonlinear lattice equations (2012)
  17. Mokhtari, Reza; Isfahani, Fereshteh Toutian; Mohammadi, Maryam: Reproducing kernel method for solving nonlinear differential-difference equations (2012)
  18. Zhao, Lei; Huang, Dingjiang; Zhou, Shuigeng: A new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the Exp-function method (2012)
  19. Zhu, Jiaofeng; Liu, Yinping: Automated derivation of the conservation laws for nonlinear differential-difference equations (2012)
  20. Gurefe, Yusuf; Misirli, Emine: New variable separation solutions of two-dimensional Burgers system (2011)

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