| Contents |
| I will present an existence result for solitary waves on a three-dimensional layer of water of finite depth. The waves are fully localised in the sense that they converge to the undisturbed state of the water in every horizontal direction. The surface tension is assumed to be weak but non-zero. The solitary-wave solutions are to leading order described by the Davey-Stewartson equation. The proof is variational in nature and relies on reducing the original water wave problem to a perturbation of the Davey-Stewartson equation. In the end, the solutions are constructed by minimising a certain functional on its natural constraint. |
|