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Exact Solutions of a High‐Order Nonlinear Wave Equation of Korteweg‐de Vries Type under Newly Solvable Conditions

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  • Weiguo Rui

Abstract

By using the integral bifurcation method together with factoring technique, we study a water wave model, a high‐order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken‐soliton solutions, periodic wave solutions of blow‐up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

Suggested Citation

  • Weiguo Rui, 2014. "Exact Solutions of a High‐Order Nonlinear Wave Equation of Korteweg‐de Vries Type under Newly Solvable Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:714214
    DOI: 10.1155/2014/714214
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    References listed on IDEAS

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    1. Khuri, S.A., 2005. "Soliton and periodic solutions for higher order wave equations of KdV type (I)," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 25-32.
    2. Weiguo Zhang & Xiang Li, 2011. "Approximate Damped Oscillatory Solutions for Generalized KdV-Burgers Equation and Their Error Estimates," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-26, September.
    3. Jae-Myoung Kim & Changbum Chun, 2012. "New Exact Solutions to the KdV-Burgers-Kuramoto Equation with the Exp-Function Method," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, May.
    4. Weiguo Zhang & Xiang Li, 2011. "Approximate Damped Oscillatory Solutions for Generalized KdV‐Burgers Equation and Their Error Estimates," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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