Rigorous justification of the modulation approximation for 2D water waves

nlsThe paper “A rigorous justification of the modulation approximation to the 2D full water wave problem“, co-authored by Nathan Totz and Sijue Wu, has been published in Communications in Mathematical Physics. The paper studies the 2D irrotational gravity wave problem, and proves error estimates for focusing NLS in Sobolev spaces.  As a consequence, existence of solutions of the water wave problem is proved in Sobolev spaces for times of order eps^{-2}.  The results are obtained directly by applying modulational analysis, normal form transformations, and the energy method.  The paper can be found here.

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