Advances in Mathematical Physics (Jan 2014)

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

  • Jiuli Yin,
  • Liuwei Zhao,
  • Shanyu Ding

DOI
https://doi.org/10.1155/2014/548920
Journal volume & issue
Vol. 2014

Abstract

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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.