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Solitary gravity water waves with an arbitrary distribution of vorticity
preprintposted on 2007-03-30, 11:08 authored by Mark D. Groves, E. Wahlen
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.
- Mathematical Sciences
NotesThis is a pre-print.