Normal Form for the Schrödinger equation with analytic non--linearities

Details Normal Form for the Schrödinger equation with analytic non--linearities Normal Form for the Schrödinger equation with analytic non--linearities

2010-12-02

arxiv.org/abs/1012.0446v6

Mathematics

Analysis of PDEs

52 pages, 2 figures

Scientific paper

In this paper we discuss a class of normal forms of the completely resonant non--linear Schr\"odinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Further analytic considerations and applications to quasi--periodic solutions will appear in a forthcoming article. This paper replaces a previous version correcting some mistakes.

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