Hi, my question is related to normal form transformations...One of the papers I would like to understand is Wu, S., "Well-posedness in Sobolev spaces of the full water wave problem in 2-D" where the author is getting ride of the quadratic nonlinearities using a normal form transformation and then a change of coordinates...I understood that the Shatah procedure, didn't fully remove the quadratic terms(in the full 2D water wave problem), but can anyone explain how that change of coordinates works?....how exactly are the quadratic terms removed?, and how she can control the residual terms (the ones that arise after the transformation....)? I have to admit that the paper is dense and I am not convinced I understood 30% of it..

Thanks! Didi