Solitary gravity water waves with an arbitrary distribution of vorticity
preprintposted on 30.03.2007, 11:08 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