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Spatial dynamics methods for solitary gravity-capillary water waves with an arbitrary distribution of vorticity
preprint
posted on 2006-10-09, 15:42 authored by Mark D. Groves, E. WahlenThis paper presents existence theories for several families of small-amplitude solitarywave
solutions to the classical water-wave problem in the presence of surface tension and
with an arbitrary distribution of vorticity. Moreover, the established local bifurcation diagram
for irrotational solitary waves is shown to remain qualitatively unchanged for any
choice of vorticity distribution.
The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system
in which the horizontal spatial direction is the time-like variable. A centre-manifold reduction
technique is employed to reduce the system to a locally equivalent Hamiltonian system
with a finite numer of degrees of freedom. Homoclinic solutions to the reduced system,
which correspond to solitary water waves, are detected by a variety of dynamical systems
methods.
History
School
- Science
Department
- Mathematical Sciences
Pages
349072 bytesPublication date
2006Notes
This is a pre-printLanguage
- en