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Solitary gravity water waves with an arbitrary distribution of vorticity
This paper presents an existence theory for small-amplitude solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an in nite-dimensional Hamiltonian system in which the...
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| Main Authors: | , |
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| Format: | Default Preprint |
| Published: |
2007
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| Subjects: | |
| Online Access: | https://hdl.handle.net/2134/2739 |
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| Summary: | This paper presents an existence theory for small-amplitude solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an in nite-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 one degree of freedom. The phase portrait of the reduced system contains a homoclinic orbit, and the corresponding solution of the water-wave problem is a solitary wave of elevation. |
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