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Exact solutions of coupled nonlinear evolution equations

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  • Yusufoğlu, Elcin
  • Bekir, Ahmet

Abstract

In this paper, we employ the tanh method for traveling wave solutions of coupled Ramani and Nizhnik–Novikov–Veselov equations. Based on the idea of the tanh method, a simple and efficient method is proposed to obtain exact solutions to the nonlinear evolution equations. The solutions obtained may be of importance in the explanation of some practical problems in physics.

Suggested Citation

  • Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:842-848
    DOI: 10.1016/j.chaos.2006.09.074
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    References listed on IDEAS

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    1. 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.
    2. Dengshan Wang & Hong-Qing Zhang, 2005. "Auto-Bäcklund Transformation And New Exact Solutions Of The(2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(03), pages 393-412.
    3. Wazwaz, Abdul-Majid, 2006. "Two reliable methods for solving variants of the KdV equation with compact and noncompact structures," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 454-462.
    4. 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.
    5. Wazwaz, Abdul-Majid & Helal, M.A., 2005. "Nonlinear variants of the BBM equation with compact and noncompact physical structures," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 767-776.
    6. Zhang, Huiqun, 2005. "New exact travelling wave solutions for some nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 921-925.
    7. Shang, Yadong, 2005. "Explicit and exact solutions for a generalized long–short wave resonance equations with strong nonlinear term," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 527-539.
    8. 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.
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    Cited by:

    1. 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.
    2. Bekir, Ahmet & Cevikel, Adem C., 2009. "New exact travelling wave solutions of nonlinear physical models," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1733-1739.
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    5. Lingxiao Li & Mingliang Wang & Jinliang Zhang, 2022. "Application of Generalized Logistic Function to Travelling Wave Solutions for a Class of Nonlinear Evolution Equations," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    6. A K M Kazi Sazzad Hossain & Md. Ali Akbar, 2017. "Closed form Solutions of New Fifth Order Nonlinear Equation and New Generalized Fifth Order Nonlinear Equation via the Enhanced (G’/G)-expansion Method," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(2), pages 19-25, December.
    7. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.

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