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 |
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Keywords
- Degasperis-Procesi equation
- coshoidal periodicwavesolutions
- Vakhnenko equation
Cite this
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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
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 -