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)

T2 - 5th International Conference on Symmetry in Nonlinear Mathematical Physics

Y2 - 23 June 2003 through 29 June 2003

ER -