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New Exact Solutions for a Higher‐Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method

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  • Yun-Mei Zhao

Abstract

In our work, a generalized KdV type equation of neglecting the highest‐order infinitesimal term, which is an important water wave model, is discussed by using the simplest equation method and its variants. The solutions obtained are general solutions which are in the form of hyperbolic, trigonometric, and rational functions. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time.

Suggested Citation

  • Yun-Mei Zhao, 2014. "New Exact Solutions for a Higher‐Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:848069
    DOI: 10.1155/2014/848069
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    References listed on IDEAS

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    1. 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).
    2. Xianbin Wu & Weiguo Rui & Xiaochun Hong, 2013. "A Generalized KdV Equation of Neglecting the Highest-Order Infinitesimal Term and Its Exact Traveling Wave Solutions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, March.
    3. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    4. Xianbin Wu & Weiguo Rui & Xiaochun Hong, 2013. "A Generalized KdV Equation of Neglecting the Highest‐Order Infinitesimal Term and Its Exact Traveling Wave Solutions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the -Dimensional Evolution Equation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, December.
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    Cited by:

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    3. Alemayehu Tamirie Deresse, 2022. "Double Sumudu Transform Iterative Method for One‐Dimensional Nonlinear Coupled Sine‐Gordon Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).

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