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Stumpons and fractal-like wave solutions to the Dullin–Gottwald–Holm equation

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  • Yin, Jiuli
  • Tian, Lixin

Abstract

The traveling wave solutions to the Dullin–Gottwald–Holm equation (called DGH equation) are classified by an improved qualitative analysis method. Meanwhile, the influence of the parameters on the traveling wave forms is specifically considered. The equation is shown to admit more traveling wave forms solutions, especially new solutions such as stumpons and fractal-like waves are first given. We also point out that the smooth solutions can converge to non-smooth ones under certain conditions. Furthermore, the new explicit forms of peakons with period are obtained.

Suggested Citation

  • Yin, Jiuli & Tian, Lixin, 2009. "Stumpons and fractal-like wave solutions to the Dullin–Gottwald–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 643-648.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:643-648
    DOI: 10.1016/j.chaos.2009.01.009
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    References listed on IDEAS

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    1. Tian, Lixin & Yin, Jiuli, 2005. "New peakon and multi-compacton solitary wave solutions of fully nonlinear sine-Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 353-363.
    2. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    3. Kalisch, Henrik & Lenells, Jonatan, 2005. "Numerical study of traveling-wave solutions for the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 287-298.
    4. Guo, Boling & Liu, Zhengrong, 2005. "Periodic cusp wave solutions and single-solitons for the b-equation," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1451-1463.
    5. Ludu, A. & Kevrekidis, P.G., 2007. "Nonlinear dispersion relations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 229-236.
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