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The tanh–coth method combined with the Riccati equation for solving non-linear equation

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  • Bekir, Ahmet

Abstract

In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh–coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.

Suggested Citation

  • Bekir, Ahmet, 2009. "The tanh–coth method combined with the Riccati equation for solving non-linear equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1467-1474.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1467-1474
    DOI: 10.1016/j.chaos.2007.09.029
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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.
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    4. Yusufoğlu, E. & Bekir, A. & Alp, M., 2008. "Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine–Cosine method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1193-1197.
    5. 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.
    6. 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.
    7. Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
    8. Wang, Tie-Ying & Ren, Yong-Hong & Zhao, Ya-Li, 2006. "Exact solutions of (3+1)-dimensional stochastic Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 920-927.
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