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Non-local symmetries and conservation laws for one-dimensional gas dynamics equations. (English) Zbl 1102.76059
Summary: The theory on the generation of conservation laws for systems of partial differential equations by the use of Lie-Bäcklund symmetries is generalised to include the non-local symmetries. It is shown how the action of a symmetry on the appropriate conservation laws can extend the symmetry generator with respect to a covering system. Systems of differential equations that describe one-dimensional gas flow are used to demonstrate the direct calculation of new non-local symmetries as well as the generation of new conservation laws. Also a solution that is invariant under a non-local symmetry is found.
MSC:
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)
76N15Gas dynamics, general