Buffoni, B.Groves, M. D.Wahlen, E.2022-05-092022-05-092022-05-092022-05-0110.1007/s00021-022-00684-5https://infoscience.epfl.ch/handle/20.500.14299/187712WOS:000786135000001Fully localised three-dimensional solitary waves are steady water waves which are evanescent in every horizontal direction. Existence theories for fully localised three-dimensional solitary waves on water of finite depth have recently been published, and in this paper we establish their existence on deep water. The governing equations are reduced to a perturbation of the two-dimensional nonlinear Schrodinger equation, which admits a family of localised solutions. Two of these solutions are symmetric in both horizontal directions and an application of a suitable variant of the implicit-function theorem shows that they persist under perturbations.Mathematics, AppliedMechanicsPhysics, Fluids & PlasmasMathematicsPhysicsexistencestabilitytext::journal::journal article::research article