TY - JOUR
T1 - Periodic solutions for a complex Hamiltonian system
T2 - New standing water-waves
AU - Agnon, Y.
AU - Glozman, M.
N1 - Funding Information:
We are grateful for the support by the US Office of Naval Research Grant N0014-91-J-1449. The heavy duty computationw as done by courtesyo f The Laboratory for Parallel Computing Researcha t Technion.
PY - 1996/9
Y1 - 1996/9
N2 - The interaction of several (up to 39) two-dimensional, deep water, gravity, standing wave modes is studied to high order (up to 18) using a Hamiltonian formulation. Four new time-periodic solutions are found. The stability of periodic standing waves to superharmonic perturbations is studied. A new instability of the standing Stokes wave is found at moderate steepness (0.266). Two of the new waves are weakly unstable. Stability of the Stokes wave to subharmonic perturbation is also studied. The long time evolution of the perturbed waves is examined. The Hamiltonian method gives most accurate results. Recurrence of the unstable Stoke waves is revealed. The periodic solutions are useful for understanding the dynamical system of the standing wave modes.
AB - The interaction of several (up to 39) two-dimensional, deep water, gravity, standing wave modes is studied to high order (up to 18) using a Hamiltonian formulation. Four new time-periodic solutions are found. The stability of periodic standing waves to superharmonic perturbations is studied. A new instability of the standing Stokes wave is found at moderate steepness (0.266). Two of the new waves are weakly unstable. Stability of the Stokes wave to subharmonic perturbation is also studied. The long time evolution of the perturbed waves is examined. The Hamiltonian method gives most accurate results. Recurrence of the unstable Stoke waves is revealed. The periodic solutions are useful for understanding the dynamical system of the standing wave modes.
UR - http://www.scopus.com/inward/record.url?scp=0000471504&partnerID=8YFLogxK
U2 - 10.1016/0165-2125(96)00011-X
DO - 10.1016/0165-2125(96)00011-X
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AN - SCOPUS:0000471504
SN - 0165-2125
VL - 24
SP - 139
EP - 150
JO - Wave Motion
JF - Wave Motion
IS - 2
ER -