Classification of linear representations of the Galilei, Poincaré, and conformal algebras in the case of a two-dimensional vector field and their applications

Abstract

We present the classification of linear representations of the Galilei, Poincaré, and conformal algebras nonequivalent under linear transformations in the case of a two-dimensional vector field. The obtained results are applied to the investigation of the symmetry properties of systems of nonlinear parabolic and hyperbolic equations.