Non-local symmetries and conservation laws for one-dimensional gas dynamics equations

摘要

The theory on the generation of conservation laws [Symmetry conditions and construction of conservation laws for differential equations, Preprint] for systems of partial differential equations by the use of Lie–Bäcklund symmetries is generalised to include the use of non-local symmetries. It is shown how the action of a symmetry on the appropriate conservation laws can be utilised to 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.