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Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Author

Listed:
  • Khaled A. Gepreel
  • Taher A. Nofal
  • Fawziah M. Alotaibi

Abstract

We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

Suggested Citation

  • Khaled A. Gepreel & Taher A. Nofal & Fawziah M. Alotaibi, 2013. "Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:756896
    DOI: 10.1155/2013/756896
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    References listed on IDEAS

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    1. Khaled A. Gepreel & A. R. Shehata, 2012. "Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, March.
    2. Khaled A. Gepreel & A. R. Shehata, 2012. "Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Wu, Guo-cheng & Xia, Tie-cheng, 2009. "A new method for constructing soliton solutions to differential-difference equation with symbolic computation," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2245-2248.
    4. Xie, Fuding & Wang, Jingquan, 2006. "A new method for solving nonlinear differential-difference equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1067-1071.
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    Cited by:

    1. Mohamed S. Mohamed & Khaled A. Gepreel & Faisal A. Al-Malki & Nouf Altalhi, 2014. "Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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