### Abstract

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

Title of host publication | Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) |

Pages | 493-497 |

Number of pages | 4 |

Volume | 50 |

Publication status | Published - 2004 |

Event | 5th International Conference on Symmetry in Nonlinear Mathematical Physics - Kiev, Ukraine Duration: 23 Jun 2003 → 29 Jun 2003 |

### Publication series

Name | Proceedings of Institute of Mathematics of NAS of Ukraine |
---|---|

Publisher | Institute of Mathematics of NAS of Ukraine |

No. | 1 |

Volume | 50 |

### Conference

Conference | 5th International Conference on Symmetry in Nonlinear Mathematical Physics |
---|---|

Abbreviated title | Symmetry 03 |

Country | Ukraine |

City | Kiev |

Period | 23/06/03 → 29/06/03 |

### Fingerprint

### Keywords

- Degasperis-Procesi equation
- coshoidal periodicwavesolutions
- Vakhnenko equation

### Cite this

*Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03)*(Vol. 50, pp. 493-497). (Proceedings of Institute of Mathematics of NAS of Ukraine; Vol. 50, No. 1).

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*Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) .*vol. 50, Proceedings of Institute of Mathematics of NAS of Ukraine, no. 1, vol. 50, pp. 493-497, 5th International Conference on Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine, 23/06/03.

**The connection of the Degasperis-Procesi equation with the Vakhnenko equation.** / Vakhnenko, Vyacheslav O.; Parkes, John.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - The connection of the Degasperis-Procesi equation with the Vakhnenko equation

AU - Vakhnenko, Vyacheslav O.

AU - Parkes, John

PY - 2004

Y1 - 2004

N2 - Travelling-wave solutions of the Degasperis-Procesi equation (DPE) are investigated. The solutions are characterized by two parameters. Hump-like, loop-like and coshoidal periodicwave solutions are found; hump-like, loop-like and peakon solitary-wave solutions are obtained as well. Hone and Wang showed a connection between the DPE and the Vakhnenko equation (VE). Comparing the solutions of the DPE and the VE, we observe that, for both equations at interaction of waves, there are three kinds of phaseshift that depend on the ratio of wave amplitudes. In particular, there is a case when two interacted waves have phaseshifts in the positive direction.

AB - Travelling-wave solutions of the Degasperis-Procesi equation (DPE) are investigated. The solutions are characterized by two parameters. Hump-like, loop-like and coshoidal periodicwave solutions are found; hump-like, loop-like and peakon solitary-wave solutions are obtained as well. Hone and Wang showed a connection between the DPE and the Vakhnenko equation (VE). Comparing the solutions of the DPE and the VE, we observe that, for both equations at interaction of waves, there are three kinds of phaseshift that depend on the ratio of wave amplitudes. In particular, there is a case when two interacted waves have phaseshifts in the positive direction.

KW - Degasperis-Procesi equation

KW - coshoidal periodicwavesolutions

KW - Vakhnenko equation

UR - http://www.imath.kiev.ua/~snmp2003/Proceedings/vakhnenko.pdf

M3 - Conference contribution book

SN - 9660232241

VL - 50

T3 - Proceedings of Institute of Mathematics of NAS of Ukraine

SP - 493

EP - 497

BT - Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03)

ER -