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New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp‐Function Method

Author

Listed:
  • Hasibun Naher
  • Farah Aini Abdullah
  • M. Ali Akbar

Abstract

We construct new analytical solutions of the (3 + 1)‐dimensional modified KdV‐Zakharov‐Kuznetsev equation by the Exp‐function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp‐function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher‐dimensional nonlinear partial differential equation.

Suggested Citation

  • Hasibun Naher & Farah Aini Abdullah & M. Ali Akbar, 2012. "New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp‐Function Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:575387
    DOI: 10.1155/2012/575387
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    References listed on IDEAS

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    1. S. M. Sayed & O. O. Elhamahmy & G. M. Gharib, 2008. "Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces," Journal of Applied Mathematics, Hindawi, vol. 2008, pages 1-10, October.
    2. S. M. Sayed & O. O. Elhamahmy & G. M. Gharib, 2008. "Travelling Wave Solutions for the KdV‐Burgers‐Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2008(1).
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    Cited by:

    1. Hong-Zhun Liu, 2013. "A Simplification for Exp‐Function Method When the Balanced Nonlinear Term Is a Certain Product," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Muhammad Shakeel & Qazi Mahmood Ul-Hassan & Jamshad Ahmad, 2014. "Applications of the Novel (G′/G)‐Expansion Method for a Time Fractional Simplified Modified Camassa‐Holm (MCH) Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)‐Dimensional Evolution Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Mingsheng Hu & Zhijuan Jia & Qiaoling Chen & Suiming Jia, 2014. "Exact Solutions for Nonlinear Wave Equations by the Exp‐Function Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Muhammad Shakeel & Qazi Mahmood Ul-Hassan & Jamshad Ahmad & Tauseef Naqvi, 2014. "Exact Solutions of the Time Fractional BBM‐Burger Equation by Novel (G′/G)‐Expansion Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    6. Hasibun Naher & Farah Aini Abdullah, 2012. "The Improved (G’/G)‐Expansion Method for the (2+1)‐Dimensional Modified Zakharov‐Kuznetsov Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Yongan Xie & Hualiang Fu & Shengqiang Tang, 2013. "Peaked and Smooth Solitons for K*(4,1) Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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