%0 Journal Article
%T Quasi-periodic solutions of the Schr£żdinger equation with arbitrary algebraic nonlinearities
%A Wei-Min Wang
%J Mathematics
%D 2009
%I arXiv
%X We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of $b$ frequencies, $b\leq d+2$, in arbitrary dimension $d$ and for arbitrary non integrable algebraic nonlinearity $p$. This reflects the conservation of $d$ momenta, energy and $L^2$ norm. In 1d, we prove the existence of quasi-periodic solutions with arbitrary $b$ and for arbitrary $p$, solving a problem that started Hamiltonian PDE.
%U http://arxiv.org/abs/0907.3409v2