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

Vyacheslav O. Vakhnenko; John Parkes

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

Vyacheslav O. Vakhnenko, John Parkes

Mathematics And Statistics

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

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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.

Original 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
Number	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

Keywords

Degasperis-Procesi equation
coshoidal periodicwavesolutions
Vakhnenko equation

Access to Document

strathprints002210Final published version, 215 KB

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

Cite this

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title = "The connection of the Degasperis-Procesi equation with the Vakhnenko equation",

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.",

keywords = "Degasperis-Procesi equation, coshoidal periodicwavesolutions, Vakhnenko equation",

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year = "2004",

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number = "1",

pages = "493--497",

booktitle = "Proceedings, 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03)",

note = "5th International Conference on Symmetry in Nonlinear Mathematical Physics, Symmetry 03 ; Conference date: 23-06-2003 Through 29-06-2003",

}

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 proceeding › Conference contribution book

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

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AU - Parkes, John

PY - 2004

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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.

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

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