Using the KAM method, we exhibit some solutions of a finite-dimensional approximation of the Zakharov Hamiltonian formulation of gravity water waves, which are spatially periodic, quasi-periodic in time, and not permanent form travelling waves. For this Hamiltonian, which is the total energy of the
On the analytic form in the frequency domain of water wave solutions
โ Scribed by M.J. Simon
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 134 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0165-2125
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โฆ Synopsis
In this paper, an analytic result due to Ursell, which applies to the radiation of water waves by a heaving semi-immersed sphere, is extended to a wide class of bodies, and to the scattering problem. This result forms the basis of a numerical method, for the computation of the hydrodynamic coefficients, which has advantages over the conventional integral equation approach.
๐ SIMILAR VOLUMES
The radius of analyticity of periodic analytic functions can be characterized by the decay of their Fourier coefficients. This observation has led to the use of socalled Gevrey norms as a simple way of estimating the time evolution of the spatial radius of analyticity of solutions to parabolic as we