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Exact solutions of KdV–Burgers’ equation by Exp-function method

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  • Soliman, A.A.

Abstract

This paper applies the Exp-function method to obtain generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computation method. The Korteweg-de Vries–Burgers (KdVB) equation is used as an example to illustrate the effectiveness of this method. The solution process is straightforward and concise, and its applications is promising for other nonlinear evolution equations.

Suggested Citation

  • Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:1034-1039
    DOI: 10.1016/j.chaos.2008.04.038
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Soliman, A.A., 2005. "Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 119-124.
    3. Doğan Kaya, 2001. "An explicit solution of coupled viscous Burgers' equation by the decomposition method," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-6, January.
    4. Soliman, A.A. & Abdou, M.A., 2007. "Exact travelling wave solutions of nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 808-815.
    5. Zhang, Sheng, 2008. "Application of Exp-function method to high-dimensional nonlinear evolution equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 270-276.
    6. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    7. El-Wakil, S.A. & Abdou, M.A., 2007. "New exact travelling wave solutions using modified extended tanh-function method," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 840-852.
    8. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    9. Soliman, A.A., 2006. "A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 294-302.
    10. El-Wakil, S.A. & Abdou, M.A., 2007. "Modified extended tanh-function method for solving nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1256-1264.
    11. Soliman, A.A., 2006. "The modified extended tanh-function method for solving Burgers-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 394-404.
    12. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
    13. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
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