Solitary waves with decaying tails propagating at the surface of a fluid are considered. Such waves are known to exist when both gravity and surface tension are included in the dynamic boundary condition. Other examples include hydroelastic waves. These solitary waves exist both in two and three dimensions. Three dimensional waves are characterised by decaying oscillations in the direction of propagation and monotonic decay in the direction perpendicular to the direction of propagation. Most of the waves previously calculated are symmetric.
In this talk we show that there are in addition many new families of nonsymmetric waves. These waves are computed for the full Euler equations in the two dimensional case. For three dimensional waves, a model equation is used.