  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.
