  In this paper we consider a class of fully nonlinear forced and reversible
Schroedinger equations and prove existence and stability of quasi-periodic
solutions. We use a Nash-Moser algorithm together with a reducibility theorem
on the linearized operator in a neighborhood of zero. Due to the presence of
the highest order derivatives in the non-linearity the classic KAM-reducibility
argument fails and one needs to use a wider class of changes of variables such
has diffeomorphisms of the torus and pseudo-differential operators. This
procedure automtically produces a change of variables, well defined on the
phase space of the equation, which diagonalizes the operator linearized at the
solution. This gives the linear stability.
