Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-time
Abstract
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 3× 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.
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