In this paper, we tried to describe the diffraction of a solitary wave by a circular island, situated within an ocean of uniform depth. So we made the following assumptions: -the fluid, initially at rest, is homogeneous, incompressible and heavy the bottom and the vertical outlines of the island are impermeable the free surface is impermeable and it is an isobar.
As a solitary wave cannot be described by means of the classic 'Poincar6's small-parameter' method, we used here the shallow-water theory. The small parameter • represents the ratio of vertical to horizontal length scales. We replaced the cylindrical coordinates r, 0, z of a particle M by the following ones:
Then, the problem amounts to calculating the function O(r,O,t) (the velocity potential, harmonic in the domain occupied by the fluid and satisfying the conditions imposed by our assumptions) and the free surface elevation denoted by z = r~ (r,O,t).
We sought the solution in the form of power series in • and we only calculated here the first approximation, by means of the Fourier transform. A numerical example was studied, allowing to illustrate our results with some curves. 1. Position du probl6me et 6quations D'une oc6an ~ fond horizontal 6merge une 11e de forrne circulaire ~ bord vertical. Le fluide oc6anique, initialernent au repos, est perturb6 par la propagation d'une onde solitaire qui est diffract6e par l'ile.