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- W2017657016 abstract "Lie point symmetries and nonlocal symmetries of partial differential equation (PDE) systems are widely used for construction of exact invariant solutions. In this paper we describe an extended algorithmic procedure that, for a given nonlocal (potential) symmetry, can yield additional exact solutions, which cannot be found using the usual algorithm. In particular, such additional solutions are exact solutions of the given PDE system, but are not invariant solutions of the corresponding potential system. As an example, we consider a tree of nonlocally related PDE systems for Lagrange planar gas dynamics equations and classify its nonlocal symmetries for an ideal polytropic gas. For two different nonlocal symmetries of the Lagrange system, we demonstrate that the extended method yields wider classes of exact solutions than the usual method." @default.
- W2017657016 created "2016-06-24" @default.
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- W2017657016 date "2008-08-01" @default.
- W2017657016 modified "2023-10-16" @default.
- W2017657016 title "An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics" @default.
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- W2017657016 doi "https://doi.org/10.1063/1.2956502" @default.
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