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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 3, Pages 647–668
(Mi smj1989)
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This article is cited in 4 scientific papers (total in 4 papers)
A property of the defining equations for the Lie algebra in the group classification problem for wave equations
S. V. Khabirov Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences, Ufa
Abstract:
We solve the group classification problem for nonlinear hyperbolic systems of differential equations. The admissible continuous group of transformations has the Lie algebra of dimension less than 5. This main statement follows from the principal property of the defining equations of the admissible Lie algebra: the commutator of two solutions is a solution. Using equivalence transformations we classify nonlinear systems in accordance with the well-known Lie algebra structures of dimension 3 and 4.
Keywords:
symmetries of differential equations, group classification, defining equations of the admissible Lie algebra.
Received: 14.11.2007
Citation:
S. V. Khabirov, “A property of the defining equations for the Lie algebra in the group classification problem for wave equations”, Sibirsk. Mat. Zh., 50:3 (2009), 647–668; Siberian Math. J., 50:3 (2009), 515–532
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https://www.mathnet.ru/eng/smj1989 https://www.mathnet.ru/eng/smj/v50/i3/p647
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Abstract page: | 335 | Full-text PDF : | 88 | References: | 65 | First page: | 5 |
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