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Double reduction of PDEs from the association of symmetries with conservation laws with applications. (English) Zbl 1116.35004
The association of conservation laws with Noether symmetries extended to Lie-Bäcklund and nonlocal symmetries has opened the possibilities to the extension of the theory on double reductions to partial differential equations that do not have a Lagrangian and therefore to not posses Noether symmetries. at the usage of the results [A. Kara, F. Mahomed, Int. J. Theor. Phys. 39, No. 1, 23–40 (2000; Zbl 0962.35009)] the author develops the theory to effect a double reduction of PDEs with two independent variables, which is possible when the PDEs admit a symmetry associated with a conservation law. This theory is illustrated by applications to the linear heat equation, the sine-Gordon and BBM equations and a system of PDEs from one dimensional gas dynamics.

35A30 Geometric theory, characteristics, transformations in context of PDEs
35L65 Hyperbolic conservation laws
58J70 Invariance and symmetry properties for PDEs on manifolds
Full Text: DOI
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