Justification of the Nonlinear Schrdinger equation for the evolution of gravity driven 2D surface water waves

In 1968 V.E. Zakharov derived the Nonlinear Schrdinger equation for the 2D water wave problem in case of no surface tension, i.e. for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. Since this time the question remained open if solutions of the 2D water wave problem behave as predicted by the Nonlinear Schrdinger equation. Here we answer this question positively.

This is joint research with C.E. Wayne (Boston)