Journal of Applied Mathematics

Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation

Bin He, Qing Meng, and Jinhua Zhang

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Abstract

By using the bifurcation method of dynamical systems and the method of phase portraits analysis, we consider a two-component Degasperis-Procesi equation: mt=-3mux-mxu+kρρx,  ρt=-ρxu+2ρux, the existence of the peakon, solitary wave and smooth periodic wave is proved, and exact parametric representations of above travelling wave solutions are obtained in different parameter regions.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 183159, 14 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808125

Digital Object Identifier
doi:10.1155/2013/183159

Mathematical Reviews number (MathSciNet)
MR3100833

Zentralblatt MATH identifier
06950544

Citation

He, Bin; Meng, Qing; Zhang, Jinhua. Bifurcations and Parametric Representations of Peakon, Solitary Wave and Smooth Periodic Wave Solutions for a Two-Component Degasperis-Procesi Equation. J. Appl. Math. 2013 (2013), Article ID 183159, 14 pages. doi:10.1155/2013/183159. https://projecteuclid.org/euclid.jam/1394808125


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