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Generalized extended tanh-function method and its application

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  • Bai, Cheng-Lin
  • Zhao, Hong

Abstract

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like, period-form solutions of nonlinear evolution equations (NEEs). Compared with most of the existing tanh-function method, extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By using this method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEEs. Make use of the method, we study the (3+1)-dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, periodic form solutions.

Suggested Citation

  • Bai, Cheng-Lin & Zhao, Hong, 2006. "Generalized extended tanh-function method and its application," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1026-1035.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:1026-1035
    DOI: 10.1016/j.chaos.2005.04.069
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    Cited by:

    1. Khani, F., 2009. "Analytic study on the higher order Ito equations: New solitary wave solutions using the Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2128-2134.
    2. Borhanifar, A. & Kabir, M.M. & Maryam Vahdat, L., 2009. "New periodic and soliton wave solutions for the generalized Zakharov system and (2+1)-dimensional Nizhnik–Novikov–Veselov system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1646-1654.
    3. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    4. Jianguo Liu & Zhifang Zeng, 2014. "Multiple soliton solutions, soliton-type solutions and rational solutions for the (3+1)-dimensional potential-YTSF equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(6), pages 989-1002, December.
    5. (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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