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Zbl 1116.35004
Sjöberg, A.
Double reduction of PDEs from the association of symmetries with conservation laws with applications. (English)
[J] Appl. Math. Comput. 184, No. 2, 608-616 (2007). ISSN 0096-3003

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 [{\it 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.
[Boris V. Loginov (Ul'yanovsk)]

MSC 2000:: *35A30 Geometric theory for PDE, transformations
35L65 Conservation laws
58J70 Invariance and symmetry properties

Keywords: partial differential equations; Lie point symmetries; conservation laws; double reduction; heat equation; BBM equation; sine-Gordon equation; one dimensional gas dynamics

Citations: Zbl 0962.35009

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