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Limiting Behavior of Travelling Waves for the Modified Degasperis‐Procesi Equation

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  • Jiuli Yin
  • Liuwei Zhao
  • Shanyu Ding

Abstract

Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis‐Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal‐like waves, double stumpons, double kinked waves, and butterfly‐like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values.

Suggested Citation

  • Jiuli Yin & Liuwei Zhao & Shanyu Ding, 2014. "Limiting Behavior of Travelling Waves for the Modified Degasperis‐Procesi Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:548920
    DOI: 10.1155/2014/548920
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    References listed on IDEAS

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    1. 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.
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