Systems of PDEs Invariant Under Galilei Group
In the present chapter we consider linear and nonlinear systems of PDEs invariant under various representations of the Galilei group and its generalizations (such as the extended Galilei group, the Schrödinger group). Sets of Sch(1,3)- and G(1,3)-nonequivalent ansatze are constructed. A wide class of linear and nonlinear Sch(1,3)-invariant systems of PDEs is described. Lame equations are studied: superalgebra of symmetry is found and a Galilei-invariant generalization is constructed. Gas dynamics and Navier-Stokes equations are considered. Exact solutions of some enumerated above equations are found.
KeywordsArbitrary Constant Schrodinger Equation Arbitrary Smooth Function Arbitrary Real Constant Final Transformation
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