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A Generalized KdV Equation of Neglecting the Highest‐Order Infinitesimal Term and Its Exact Traveling Wave Solutions

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  • Xianbin Wu
  • Weiguo Rui
  • Xiaochun Hong

Abstract

We study a generalized KdV equation of neglecting the highest order infinitesimal term, which is an important water wave model. Some exact traveling wave solutions such as singular solitary wave solutions, semiloop soliton solutions, dark soliton solutions, dark peakon solutions, dark loop‐soliton solutions, broken loop‐soliton solutions, broken wave solutions of U‐form and C‐form, periodic wave solutions of singular type, and broken wave solution of semiparabola form are obtained. By using mathematical software Maple, we show their profiles and discuss their dynamic properties. Investigating these properties, we find that the waveforms of some traveling wave solutions vary with changes of certain parameters.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:656297
    DOI: 10.1155/2013/656297
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    References listed on IDEAS

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    1. Bi, Qinsheng, 2007. "Peaked singular wave solutions associated with singular curves," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 417-423.
    2. 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.
    3. 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.
    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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    Cited by:

    1. 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).
    2. Yun Wu & Zhengrong Liu, 2013. "New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel‐Korteweg‐de Vries Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. 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).

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