Nonlinear evolution equations invariant under the Schrodinger group in three-dimensional spacetime

A classification of all possible realizations of the Galilei, Galilei-simil itude and Schrodinger Lie algebras in three-dimensional spacetime in terms of vector fields under the action of the group of local diffeomorphisms of the space R-3 x C is presented. Using this result a variety of second-order evolution equations invariant under the corresponding groups are construct ed and their physical significance is discussed.