Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy, which is given in dimensionl