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

Vyacheslav O. Vakhnenko, John Parkes

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Abstract

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.
LanguageEnglish
Title of host publication Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03)
Pages493-497
Number of pages4
Volume50
Publication statusPublished - 2004
Event5th International Conference on Symmetry in Nonlinear Mathematical Physics - Kiev, Ukraine
Duration: 23 Jun 200329 Jun 2003

Publication series

NameProceedings of Institute of Mathematics of NAS of Ukraine
PublisherInstitute of Mathematics of NAS of Ukraine
No.1
Volume50

Conference

Conference5th International Conference on Symmetry in Nonlinear Mathematical Physics
Abbreviated titleSymmetry 03
CountryUkraine
CityKiev
Period23/06/0329/06/03

Fingerprint

Degasperis-Procesi Equation
Peakon
Solitary Wave Solution
Traveling Wave Solutions
Phase Shift
Two Parameters
Interaction

Keywords

  • Degasperis-Procesi equation
  • coshoidal periodicwavesolutions
  • Vakhnenko equation

Cite this

Vakhnenko, V. O., & Parkes, J. (2004). The connection of the Degasperis-Procesi equation with the Vakhnenko equation. In 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).
Vakhnenko, Vyacheslav O. ; Parkes, John. / The connection of the Degasperis-Procesi equation with the Vakhnenko equation. Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) . Vol. 50 2004. pp. 493-497 (Proceedings of Institute of Mathematics of NAS of Ukraine; 1).
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abstract = "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.",
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Vakhnenko, VO & Parkes, J 2004, The connection of the Degasperis-Procesi equation with the Vakhnenko equation. in 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.

Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) . Vol. 50 2004. p. 493-497 (Proceedings of Institute of Mathematics of NAS of Ukraine; Vol. 50, No. 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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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.

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Vakhnenko VO, Parkes J. The connection of the Degasperis-Procesi equation with the Vakhnenko equation. In Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03) . Vol. 50. 2004. p. 493-497. (Proceedings of Institute of Mathematics of NAS of Ukraine; 1).