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Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation

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  • Jiangbo Zhou
  • Lixin Tian

Abstract

We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation . The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.

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  • Jiangbo Zhou & Lixin Tian, 2009. "Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-13, June.
    • Handle: RePEc:hin:jnlmpe:249361
    DOI: 10.1155/2009/249361
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