Spatial Dynamics Methods for Solitary Gravity-Capillary Water Waves with an Arbitrary Distribution of Vorticity
Author
Summary, in English
This paper presents existence theories for several families of small-amplitude solitary-wave solutions to the classical two-dimensional 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 timelike variable. A center-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number 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.
Department/s
- Mathematics (Faculty of Sciences)
- Partial differential equations
Publishing year
2007
Language
English
Pages
932-964
Publication/Series
SIAM Journal on Mathematical Analysis
Volume
39
Issue
3
Document type
Journal article
Publisher
Society for Industrial and Applied Mathematics
Topic
- Mathematics
Keywords
- capillarity
- water waves
- vorticity
- bifurcation theory
Status
Published
Research group
- Partial differential equations
ISBN/ISSN/Other
- ISSN: 0036-1410