  A classification of all possible realizations of the Galilei,
Galilei-similitude and Schroedinger Lie algebras in three-dimensional
space-time in terms of vector fields under the action of the group of local
diffeomorphisms of the space $\R^3\times\C$ is presented. Using this result a
variety of general second order evolution equations invariant under the
corresponding groups are constructed and their physical significance are
discussed.
