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

Abstract

A classification of all possible realizations of the Galilei, Galilei-similitude and Schrödinger Lie algebras in three-dimensional spacetime in terms of vector fields under the action of the group of local diffeomorphisms of the space is presented. Using this result a variety of second-order evolution equations invariant under the corresponding groups are constructed and their physical significance is discussed.