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Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Author

Listed:
  • Khaled A. Gepreel
  • A. R. Shehata

Abstract

We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:710375
    DOI: 10.1155/2012/710375
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    References listed on IDEAS

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    1. Liu, Cheng-shi, 2009. "Exponential function rational expansion method for nonlinear differential–difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 708-716.
    2. 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.
    3. Wang, Qi & Yu, Yaxuan, 2006. "New rational formal solutions for (1+1)-dimensional Toda equation and another Toda equation," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 904-915.
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    Cited by:

    1. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)‐Dimensional Evolution Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Hasibun Naher & Farah Aini Abdullah, 2012. "The Improved (G’/G)‐Expansion Method for the (2+1)‐Dimensional Modified Zakharov‐Kuznetsov Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Fanwei Meng, 2013. "A New Variable‐Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Khaled A. Gepreel, 2013. "Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. 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).

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