### Abstract

Language | English |
---|---|

Pages | 1309-1316 |

Number of pages | 7 |

Journal | Chaos, Solitons and Fractals |

Volume | 26 |

Issue number | 5 |

DOIs | |

Publication status | Published - Dec 2005 |

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### Keywords

- Camassa–Holm equation
- solitons
- finite element analysis
- numerical mathematics

### Cite this

*Chaos, Solitons and Fractals*,

*26*(5), 1309-1316. https://doi.org/10.1016/j.chaos.2005.03.011

}

*Chaos, Solitons and Fractals*, vol. 26, no. 5, pp. 1309-1316. https://doi.org/10.1016/j.chaos.2005.03.011

**Explicit solutions of the Camassa-Holm equation.** / Parkes, E.J.; Vakhnenko, V.O.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Explicit solutions of the Camassa-Holm equation

AU - Parkes, E.J.

AU - Vakhnenko, V.O.

PY - 2005/12

Y1 - 2005/12

N2 - Explicit travelling-wave solutions of the Camassa-Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis-Procesi equation are given in an appendix.

AB - Explicit travelling-wave solutions of the Camassa-Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis-Procesi equation are given in an appendix.

KW - Camassa–Holm equation

KW - solitons

KW - finite element analysis

KW - numerical mathematics

UR - http://www.maths.strath.ac.uk/~caas35/p&vCSF05.pdf

UR - http://dx.doi.org/10.1016/j.chaos.2005.03.011

U2 - 10.1016/j.chaos.2005.03.011

DO - 10.1016/j.chaos.2005.03.011

M3 - Article

VL - 26

SP - 1309

EP - 1316

JO - Chaos, Solitons and Fractals

T2 - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 5

ER -