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EXP-function method and its application to nonlinear equations

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  • (Benn)Wu, Xu-Hong
  • He, Ji-Huan

Abstract

Exp-function method is used to find a unified solution of a nonlinear wave equation. Variant Boussinesq equations are selected to illustrate the effectiveness and simplicity of the method. A generalized solitary solution with free parameters is obtained.

Suggested Citation

  • (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.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:3:p:903-910
    DOI: 10.1016/j.chaos.2007.01.024
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Limit cycle and bifurcation of nonlinear problems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 827-833.
    2. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    3. Bai, Cheng-Lin & Zhao, Hong, 2006. "Generalized extended tanh-function method and its application," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1026-1035.
    4. Wang, Dengshan & Zhang, Hong-Qing, 2005. "Further improved F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 601-610.
    5. 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.
    6. Ibrahim, R.S. & El-Kalaawy, O.H., 2007. "Extended tanh-function method and reduction of nonlinear Schrödinger-type equations to a quadrature," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1001-1008.
    7. Ren, Yu-Jie & Zhang, Hong-Qing, 2006. "A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 959-979.
    8. 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.
    9. Zhao, Xiqiang & Wang, Limin & Sun, Weijun, 2006. "The repeated homogeneous balance method and its applications to nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 448-453.
    10. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    11. Wazwaz, Abdul-Majid, 2005. "The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 55-63.
    12. Hon, Y.C. & Fan, Engui, 2005. "Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1087-1096.
    13. Yomba, Emmanuel, 2005. "The modified extended Fan’s sub-equation method and its application to (2+1)-dimensional dispersive long wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 785-794.
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    Cited by:

    1. Bekir, Ahmet & Boz, Ahmet, 2009. "Application of Exp-function method for (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 458-465.
    2. Nguyen, Lu Trong Khiem, 2015. "Modified homogeneous balance method: Applications and new solutions," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 148-155.
    3. Valery Ochkov & Inna Vasileva & Yulia Chudova & Anton Tikhonov, 2023. "About Oscillations in Nonlinear Systems with Elastic Bonds," Mathematics, MDPI, vol. 11(8), pages 1-13, April.
    4. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    5. Erbaş, Barış & Yusufoğlu, Elçin, 2009. "Exp-function method for constructing exact solutions of Sharma–Tasso–Olver equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2326-2330.

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