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New Exact Solutions for a Higher Order Wave Equation of KdV Type Using Multiple G′/G‐Expansion Methods

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  • Yinghui He

Abstract

The G′/G‐expansion method is a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems. In our work, exact traveling wave solutions of a generalized KdV type equation of neglecting the highest order infinitesimal term, which is an important water wave model, are discussed by the G′/G‐expansion method and its variants. As a result, many new exact solutions involving parameters, expressed by Jacobi elliptic functions, hyperbolic functions, trigonometric function, and the rational functions, are obtained. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time. The related results are enriched.

Suggested Citation

  • Yinghui He, 2014. "New Exact Solutions for a Higher Order Wave Equation of KdV Type Using Multiple G′/G‐Expansion Methods," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:148132
    DOI: 10.1155/2014/148132
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    References listed on IDEAS

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    1. 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.
    2. Marianna Ruggieri, 2012. "Kink Solutions for a Class of Generalized Dissipative Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, November.
    3. 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).
    4. Marianna Ruggieri, 2012. "Kink Solutions for a Class of Generalized Dissipative Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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