No solitary waves exist on 2D deep water
  The solitary wave problem at the free surface of a two-dimensional, infinitely-deep and irrotational flow of water, under the influence of gravity, is formulated as a nonlinear pseudodifferential equation. A Pohozaev identity is used to show that it admits no solutions which asymptotically vanish faster than linearly. 
Vera Mikyoung Hur
math.AP math-ph math.MP physics.flu-dyn