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 -