Nonlinear Evolution Equations Invariant Under Schroedinger Group in   three-dimensional Space-time
  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. 
Faruk Gungor