## Journal of Applied Mathematics

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

#### Abstract

By using the bifurcation method of dynamical systems and the method of phase portraits analysis, we consider a two-component Degasperis-Procesi equation: ${m}_{t}=-\mathrm{3}m{u}_{x}-{m}_{x}u+k\rho {\rho }_{x}, \mathrm{}{\rho }_{t}=-{\rho }_{x}u+\mathrm{2}\rho {u}_{x},$ 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

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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