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A New Variable‐Coefficient Riccati Subequation Method for Solving Nonlinear Lattice Equations

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  • Fanwei Meng

Abstract

We propose a new variable‐coefficient Riccati subequation method to establish new exact solutions for nonlinear differential‐difference equations. For illustrating the validity of this method, we apply it to the discrete (2 + 1)‐dimensional Toda lattice equation. As a result, some new and generalized traveling wave solutions including hyperbolic function solutions, trigonometric function solutions, and rational function solutions are obtained.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:810363
    DOI: 10.1155/2013/810363
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    References listed on IDEAS

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    1. Huang, Wenhua & Liu, Yulu, 2009. "Jacobi elliptic function solutions of the Ablowitz–Ladik discrete nonlinear Schrödinger system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 786-792.
    2. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    3. 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.
    4. Liu, Cheng-shi, 2009. "Exponential function rational expansion method for nonlinear differential–difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 708-716.
    5. 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).
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