A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension
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 has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as ‘lumps’), and a mathematically rigorous existence theory for strong surfac