Fully localised three-dimensional gravity-capillary solitary waves on water of infinite depth
arXiv:2108.05973 · doi:10.1007/s00021-022-00684-5
Abstract
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently been established, and in this article we present an existence theory for water of infinite depth. The governing equations are reduced to a perturbation of the two-dimensional nonlinear Schrödinger equation, which admits a family of localised solutions. Two of these solutions are symmetric in both horizontal directions and an application of a suitable version of the implicit-function theorem shows that they persist under perturbations.
arXiv comment24 pages. arXiv admin note: text overlap with arXiv:1603.09189
References in corpus (3)
- Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
- A variational reduction and the existence of a fully-localised solitary wave for the three-dimensional water-wave problem with weak surface tension
- Integral and asymptotic properties of solitary waves in deep water